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Stochastic Chemical Kinetics
by Péter Érdi Gábor LenteThis volume reviews the theory and simulation methods of stochastic kinetics by integrating historical and recent perspectives, presents applications, mostly in the context of systems biology and also in combustion theory. In recent years, due to the development in experimental techniques, such as optical imaging, single cell analysis, and fluorescence spectroscopy, biochemical kinetic data inside single living cells have increasingly been available. The emergence of systems biology brought renaissance in the application of stochastic kinetic methods.
Stochastic Communities: A Mathematical Theory of Biodiversity
by A. DewdneyStochastic Communities presents a theory of biodiversity by analyzing the distribution of abundances among species in the context of a community. The basis of this theory is a distribution called the "J distribution." This distribution is a pure hyperbola and mathematically implied by the "stochastic species hypothesis" assigning equal probabilities of birth and death within the population of each species over varying periods of time. The J distribution in natural communities has strong empirical support resulting from a meta-study and strong theoretical support from a theorem that is mathematically implied by the stochastic species hypothesis.
Stochastic Control in Discrete and Continuous Time
by Atle SeierstadThis book provides a comprehensive introduction to stochastic control problems in discrete and continuous time. The material is presented logically, beginning with the discrete-time case using few mathematical tools before proceeding to the stochastic continuous-time models requiring more advanced mathematics. Topics covered include stochastic maximum principles for discrete time, continuous time, and for problems with terminal conditions. A nonstandard treatment of piecewise deterministic problems, related to some control problems, is also presented. Numerous illustrative examples and exercises are included to enhance the understanding of the reader. By interlinking many fields in stochastic control, the material gives the student the opportunity to see the connections between different fields and the underlying ideas that unify them. This text will be of benefit to students in economics, engineering, applied mathematics and related fields. Prerequisites include a course in calculus and elementary probability theory.
Stochastic Control Theory
by Makiko NisioThis book offers a systematic introduction to the optimal stochastic control theory via the dynamic programming principle, which is a powerful tool to analyze control problems. First we consider completely observable control problems with finite horizons. Using a time discretization we construct a nonlinear semigroup related to the dynamic programming principle (DPP), whose generator provides the Hamilton-Jacobi-Bellman (HJB) equation, and we characterize the value function via the nonlinear semigroup, besides the viscosity solution theory. When we control not only the dynamics of a system but also the terminal time of its evolution, control-stopping problems arise. This problem is treated in the same frameworks, via the nonlinear semigroup. Its results are applicable to the American option price problem. Zero-sum two-player time-homogeneous stochastic differential games and viscosity solutions of the Isaacs equations arising from such games are studied via a nonlinear semigroup related to DPP (the min-max principle, to be precise). Using semi-discretization arguments, we construct the nonlinear semigroups whose generators provide lower and upper Isaacs equations. Concerning partially observable control problems, we refer to stochastic parabolic equations driven by colored Wiener noises, in particular, the Zakai equation. The existence and uniqueness of solutions and regularities as well as Itô's formula are stated. A control problem for the Zakai equations has a nonlinear semigroup whose generator provides the HJB equation on a Banach space. The value function turns out to be a unique viscosity solution for the HJB equation under mild conditions. This edition provides a more generalized treatment of the topic than does the earlier book Lectures on Stochastic Control Theory (ISI Lecture Notes 9), where time-homogeneous cases are dealt with. Here, for finite time-horizon control problems, DPP was formulated as a one-parameter nonlinear semigroup, whose generator provides the HJB equation, by using a time-discretization method. The semigroup corresponds to the value function and is characterized as the envelope of Markovian transition semigroups of responses for constant control processes. Besides finite time-horizon controls, the book discusses control-stopping problems in the same frameworks.
Stochastic Differential Equations: An Introduction with Applications in Population Dynamics Modeling
by Michael J. PanikA beginner’s guide to stochastic growth modeling The chief advantage of stochastic growth models over deterministic models is that they combine both deterministic and stochastic elements of dynamic behaviors, such as weather, natural disasters, market fluctuations, and epidemics. This makes stochastic modeling a powerful tool in the hands of practitioners in fields for which population growth is a critical determinant of outcomes. However, the background requirements for studying SDEs can be daunting for those who lack the rigorous course of study received by math majors. Designed to be accessible to readers who have had only a few courses in calculus and statistics, this book offers a comprehensive review of the mathematical essentials needed to understand and apply stochastic growth models. In addition, the book describes deterministic and stochastic applications of population growth models including logistic, generalized logistic, Gompertz, negative exponential, and linear. Ideal for students and professionals in an array of fields including economics, population studies, environmental sciences, epidemiology, engineering, finance, and the biological sciences, Stochastic Differential Equations: An Introduction with Applications in Population Dynamics Modeling: • Provides precise definitions of many important terms and concepts and provides many solved example problems • Highlights the interpretation of results and does not rely on a theorem-proof approach • Features comprehensive chapters addressing any background deficiencies readers may have and offers a comprehensive review for those who need a mathematics refresher • Emphasizes solution techniques for SDEs and their practical application to the development of stochastic population models An indispensable resource for students and practitioners with limited exposure to mathematics and statistics, Stochastic Differential Equations: An Introduction with Applications in Population Dynamics Modeling is an excellent fit for advanced undergraduates and beginning graduate students, as well as practitioners who need a gentle introduction to SDEs. Michael J. Panik, PhD, is Professor in the Department of Economics, Barney School of Business and Public Administration at the University of Hartford in Connecticut. He received his PhD in Economics from Boston College and is a member of the American Mathematical Society, The American Statistical Association, and The Econometric Society.
Stochastic Differential Equations and Applications (Dover Books on Mathematics)
by Prof. Avner FriedmanThis text develops the theory of systems of stochastic differential equations, and it presents applications in probability, partial differential equations, and stochastic control problems. Originally published in two volumes, it combines a book of basic theory and selected topics with a book of applications.The first part explores Markov processes and Brownian motion; the stochastic integral and stochastic differential equations; elliptic and parabolic partial differential equations and their relations to stochastic differential equations; the Cameron-Martin-Girsanov theorem; and asymptotic estimates for solutions. The section concludes with a look at recurrent and transient solutions.Volume 2 begins with an overview of auxiliary results in partial differential equations, followed by chapters on nonattainability, stability and spiraling of solutions; the Dirichlet problem for degenerate elliptic equations; small random perturbations of dynamical systems; and fundamental solutions of degenerate parabolic equations. Final chapters examine stopping time problems and stochastic games and stochastic differential games. Problems appear at the end of each chapter, and a familiarity with elementary probability is the sole prerequisite.
Stochastic Differential Equations, Backward SDEs, Partial Differential Equations
by Etienne Pardoux Aurel RăşcanuThis research monograph presents results to researchers in stochastic calculus, forward and backward stochastic differential equations, connections between diffusion processes and second order partial differential equations (PDEs), and financial mathematics. It pays special attention to the relations between SDEs/BSDEs and second order PDEs under minimal regularity assumptions, and also extends those results to equations with multivalued coefficients. The authors present in particular the theory of reflected SDEs in the above mentioned framework and include exercises at the end of each chapter. Stochastic calculus and stochastic differential equations (SDEs) were first introduced by K. Itô in the 1940s, in order to construct the path of diffusion processes (which are continuous time Markov processes with continuous trajectories taking their values in a finite dimensional vector space or manifold), which had been studied from a more analytic point of view by Kolmogorov in the 1930s. Since then, this topic has become an important subject of Mathematics and Applied Mathematics, because of its mathematical richness and its importance for applications in many areas of Physics, Biology, Economics and Finance, where random processes play an increasingly important role. One important aspect is the connection between diffusion processes and linear partial differential equations of second order, which is in particular the basis for Monte Carlo numerical methods for linear PDEs. Since the pioneering work of Peng and Pardoux in the early 1990s, a new type of SDEs called backward stochastic differential equations (BSDEs) has emerged. The two main reasons why this new class of equations is important are the connection between BSDEs and semilinear PDEs, and the fact that BSDEs constitute a natural generalization of the famous Black and Scholes model from Mathematical Finance, and thus offer a natural mathematical framework for the formulation of many new models in Finance.
Stochastic Differential Equations for Science and Engineering
by Uffe Høgsbro ThygesenStochastic Differential Equations for Science and Engineering is aimed at students at the M.Sc. and PhD level. The book describes the mathematical construction of stochastic differential equations with a level of detail suitable to the audience, while also discussing applications to estimation, stability analysis, and control. The book includes numerous examples and challenging exercises. Computational aspects are central to the approach taken in the book, so the text is accompanied by a repository on GitHub containing a toolbox in R which implements algorithms described in the book, code that regenerates all figures, and solutions to exercises. Features: Contains numerous exercises, examples, and applications Suitable for science and engineering students at Master’s or PhD level Thorough treatment of the mathematical theory combined with an accessible treatment of motivating examples GitHub repository available at: https://github.com/Uffe-H-Thygesen/SDEbook and https://github.com/Uffe-H-Thygesen/SDEtools
Stochastic Differential Inclusions and Applications
by Michał KisielewiczThis book aims to further develop the theory of stochastic functional inclusions and their applications for describing the solutions of the initial and boundary value problems for partial differential inclusions. The self-contained volume is designed to introduce the reader in a systematic fashion, to new methods of the stochastic optimal control theory from the very beginning. The exposition contains detailed proofs and uses new and original methods to characterize the properties of stochastic functional inclusions that, up to the present time, have only been published recently by the author. The work is divided into seven chapters, with the first two acting as an introduction, containing selected material dealing with point- and set-valued stochastic processes, and the final two devoted to applications and optimal control problems. The book presents recent and pressing issues in stochastic processes, control, differential games, optimization and their application in finance, manufacturing, queueing networks, and climate control. Written by an award-winning author in the field of stochastic differential inclusions and their application to control theory, This book is intended for students and researchers in mathematics and applications; particularly those studying optimal control theory. It is also highly relevant for students of economics and engineering. The book can also be used as a reference on stochastic differential inclusions. Knowledge of select topics in analysis and probability theory are required.
Stochastic Discounted Cash Flow: A Theory of the Valuation of Firms (Springer Texts in Business and Economics)
by Andreas Löffler Lutz KruschwitzThis open access book discusses firm valuation, which is of interest to economists, particularly those working in finance. Firm valuation comes down to the calculation of the discounted cash flow, often only referred to by its abbreviation, DCF. There are, however, different coexistent versions, which seem to compete against each other, such as entity approaches and equity approaches. Acronyms are often used, such as APV (adjusted present value) or WACC (weighted average cost of capital), two concepts classified as entity approaches.This book explains why there are several procedures and whether they lead to the same result. It also examines the economic differences between the methods and indicates the various purposes they serve. Further it describes the limits of the procedures and the situations they are best applied to. The problems this book addresses are relevant to theoreticians and practitioners alike.
Stochastic Dominance
by Haim LevyThis fully updated third edition is devoted to the analysis of various Stochastic Dominance (SD) decision rules. It discusses the pros and cons of each of the alternate SD rules, the application of these rules to various research areas like statistics, agriculture, medicine, measuring income inequality and the poverty level in various countries, and of course, to investment decision-making under uncertainty. The book features changes and additions to the various chapters, and also includes two completely new chapters. One deals with asymptotic SD and the relation between FSD and the maximum geometric mean (MGM) rule (or the maximum growth portfolio). The other new chapter discusses bivariate SD rules where the individual's utility is determined not only by his own wealth, but also by his standing relative to his peer group. Stochastic Dominance: Investment Decision Making under Uncertainty, 3rd Ed. covers the following basic issues: the SD approach, asymptotic SD rules, the mean-variance (MV) approach, as well as the non-expected utility approach. The non-expected utility approach focuses on Regret Theory (RT) and mainly on prospect theory (PT) and its modified version, cumulative prospect theory (CPT) which assumes S-shape preferences. In addition to these issues the book suggests a new stochastic dominance rule called the Markowitz stochastic dominance (MSD) rule corresponding to all reverse-S-shape preferences. It also discusses the concept of the multivariate expected utility and analyzed in more detail the bivariate expected utility case. From the reviews of the second edition: "This book is an economics book about stochastic dominance. . . . is certainly a valuable reference for graduate students interested in decision making under uncertainty. It investigates and compares different approaches and presents many examples. Moreover, empirical studies and experimental results play an important role in this book, which makes it interesting to read. " (Nicole Bäuerle, Mathematical Reviews, Issue 2007 d)
Stochastic Dynamic Response and Stability of Ships and Offshore Platforms (Ocean Engineering & Oceanography #27)
by Yingguang WangThis textbook investigates in detail the methods for stochastic dynamic response and stability analyses of nonlinear systems (especially ships and ocean engineering systems), elucidating the advantages and disadvantages of each of the methods (the statistical linearization method, the perturbation method, the Monte Carlo Simulation method, the numerical path integration method, the global geometric method and the first passage theory). Studies on stochastic dynamic analysis of nonlinear systems have attracted engineers and scientists from various disciplines, such as aeronautical, civil, mechanical and ocean engineering. Pursuing a systematic approach, this book establishes a fundamental framework for this topic, while emphasizing the importance of accurate and efficient analysis as well as the significant influence of choosing a suitable method in the design and optimization of various nonlinear engineering systems (especially ships and ocean engineering systems).The textbook is intended for upper undergraduate and graduate students who are interested in advanced dynamic analysis technologies, researchers investigating nonlinear systems under stochastic dynamic excitations, and civil/mechanical/structural/ocean engineers working on designing and optimization of real-world nonlinear engineering systems. The basis of English translation of this book from its Chinese original manuscript was done with the help of artificial intelligence. A subsequent human revision of the content was done by the author.
Stochastic Dynamics in Computational Biology (Frontiers in Applied Dynamical Systems: Reviews and Tutorials #8)
by Stefanie Winkelmann Christof SchütteThe aim of this book is to provide a well-structured and coherent overview of existing mathematical modeling approaches for biochemical reaction systems, investigating relations between both the conventional models and several types of deterministic-stochastic hybrid model recombinations. Another main objective is to illustrate and compare diverse numerical simulation schemes and their computational effort. Unlike related works, this book presents a broad scope in its applications, from offering a detailed introduction to hybrid approaches for the case of multiple population scales to discussing the setting of time-scale separation resulting from widely varying firing rates of reaction channels. Additionally, it also addresses modeling approaches for non well-mixed reaction-diffusion dynamics, including deterministic and stochastic PDEs and spatiotemporal master equations. Finally, by translating and incorporating complex theory to a level accessible to non-mathematicians, this book effectively bridges the gap between mathematical research in computational biology and its practical use in biological, biochemical, and biomedical systems.
Stochastic Dynamics of Marine Structures
by Arvid Naess Torgeir MoanStochastic Dynamics of Marine Structures is a text for students and reference for professionals on the basic theory and methods used for stochastic modeling and analysis of marine structures subjected to environmental loads. The first part of the book provides a detailed introduction to the basic dynamic analysis of structures, which serves as a foundation for later chapters on stochastic response analysis. This includes an extensive chapter on the finite element method. A careful introduction to stochastic modeling is provided, which includes the concepts: stochastic process, variance spectrum, random environmental processes, response spectrum, response statistics, and short- and long-term extreme value models. The second part of the book offers detailed discussions of limit state design approaches, fatigue design methods, the equations of motion for dynamic structures, and numerical solution techniques. The final chapter highlights methods for prediction of extreme values from measured data or data obtained by Monte Carlo simulation.
Stochastic Dynamics of Structures
by Abdelkhalak El Hami Bouchaib RadiThis book is dedicated to the general study of the dynamics of mechanical structures with consideration of uncertainties. The goal is to get the appropriate forms of a part in minimizing a given criterion. In all fields of structural mechanics, the impact of good design of a room is very important to its strength, its life and its use in service. The development of the engineer's art requires considerable effort to constantly improve structural design techniques.
Stochastic Dynamics Out of Equilibrium: Institut Henri Poincaré, Paris, France, 2017 (Springer Proceedings in Mathematics & Statistics #282)
by Giambattista Giacomin Stefano Olla Ellen Saada Herbert Spohn Gabriel StoltzStemming from the IHP trimester "Stochastic Dynamics Out of Equilibrium", this collection of contributions focuses on aspects of nonequilibrium dynamics and its ongoing developments.It is common practice in statistical mechanics to use models of large interacting assemblies governed by stochastic dynamics. In this context "equilibrium" is understood as stochastically (time) reversible dynamics with respect to a prescribed Gibbs measure. Nonequilibrium dynamics correspond on the other hand to irreversible evolutions, where fluxes appear in physical systems, and steady-state measures are unknown.The trimester, held at the Institut Henri Poincaré (IHP) in Paris from April to July 2017, comprised various events relating to three domains (i) transport in non-equilibrium statistical mechanics; (ii) the design of more efficient simulation methods; (iii) life sciences. It brought together physicists, mathematicians from many domains, computer scientists, as well as researchers working at the interface between biology, physics and mathematics.The present volume is indispensable reading for researchers and Ph.D. students working in such areas.
Stochastic Equations for Complex Systems
by Stefan Heinz Hakima BessaihMathematical analyses and computational predictions of the behavior of complex systems are needed to effectively deal with weather and climate predictions, for example, and the optimal design of technical processes. Given the random nature of such systems and the recognized relevance of randomness, the equations used to describe such systems usually need to involve stochastics. The basic goal of this book is to introduce the mathematics and application of stochastic equations used for the modeling of complex systems. A first focus is on the introduction to different topics in mathematical analysis. A second focus is on the application of mathematical tools to the analysis of stochastic equations. A third focus is on the development and application of stochastic methods to simulate turbulent flows as seen in reality. This book is primarily oriented towards mathematics and engineering PhD students, young and experienced researchers, and professionals working in the area of stochastic differential equations and their applications. It contributes to a growing understanding of concepts and terminology used by mathematicians, engineers, and physicists in this relatively young and quickly expanding field.
Stochastic Equations in Infinite Dimensions
by Giuseppe Da PratoThe aim of this book is to give a systematic and self-contained presentation of basic results on stochastic evolution equations in infinite dimensional, typically Hilbert and Banach, spaces. These are a generalization of stochastic differential equations as introduced by Itô and Gikham that occur, for instance, when describing random phenomena that crop up in science and engineering, as well as in the study of differential equations. The book is divided into three parts. In the first the authors give a self-contained exposition of the basic properties of probability measure on separable Banach and Hilbert spaces, as required later; they assume a reasonable background in probability theory and finite dimensional stochastic processes. The second part is devoted to the existence and uniqueness of solutions of a general stochastic evolution equation, and the third concerns the qualitative properties of those solutions. Appendices gather together background results from analysis that are otherwise hard to find under one roof. The book ends with a comprehensive bibliography that will contribute to the book's value for all working in stochastic differential equations.
Stochastic Foundations in Movement Ecology
by Vicenç Méndez Daniel Campos Frederic BartumeusThis book presents the fundamental theory for non-standard diffusion problems in movement ecology. Lévy processes and anomalous diffusion have shown to be both powerful and useful tools for qualitatively and quantitatively describing a wide variety of spatial population ecological phenomena and dynamics, such as invasion fronts and search strategies. Adopting a self-contained, textbook-style approach, the authors provide the elements of statistical physics and stochastic processes on which the modeling of movement ecology is based and systematically introduce the physical characterization of ecological processes at the microscopic, mesoscopic and macroscopic levels. The explicit definition of these levels and their interrelations is particularly suitable to coping with the broad spectrum of space and time scales involved in bio-ecological problems. Including numerous exercises (with solutions), this text is aimed at graduate students and newcomers in this field at the interface of theoretical ecology, mathematical biology and physics.
Stochastic Frontier Analysis
by Subal C. Kumbhakar C. A. Knox LovellModern textbook presentations of production economics typically treat producers as successful optimizers. Conventional econometric practice has generally followed this paradigm, and least squares based regression techniques have been used to estimate production, cost, profit and other functions. In such a framework deviations from maximum output, from minimum cost and cost minimizing input demands, and from maximum profit and profit maximizing output supplies and input demands, are attributed exclusively to random statistical noise. However casual empiricism and the business press both make persuasive cases for the argument that, although producers may indeed attempt to optimize, they do not always succeed. This book develops econometric techniques for the estimation of production, cost and profit frontiers, and for the estimation of the technical and economic efficiency with which producers approach these frontiers. Since these frontiers envelop rather than intersect the data, and since the authors continue to maintain the traditional econometric belief in the presence of external forces contributing to random statistical noise, the work is titled Stochastic Frontier Analysis.
Stochastic Game Strategies and their Applications
by Bor-Sen ChenGame theory involves multi-person decision making and differential dynamic game theory has been widely applied to n-person decision making problems, which are stimulated by a vast number of applications. This book addresses the gap to discuss general stochastic n-person noncooperative and cooperative game theory with wide applications to control systems, signal processing systems, communication systems, managements, financial systems, and biological systems. H∞ game strategy, n-person cooperative and noncooperative game strategy are discussed for linear and nonlinear stochastic systems along with some computational algorithms developed to efficiently solve these game strategies.
Stochastic Games and Related Concepts (HBA Lecture Notes in Mathematics #2)
by T. Parthasarathy Sujatha BabuThis book discusses stochastic game theory and related concepts. Topics focused upon in the book include matrix games, finite, infinite, and undiscounted stochastic games, n-player cooperative games, minimax theorem, and more. In addition to important definitions and theorems, the book provides readers with a range of problem-solving techniques and exercises. This book is of value to graduate students and readers of probability and statistics alike.
Stochastic Geometry: Modern Research Frontiers (Lecture Notes in Mathematics #2237)
by David CoupierThis volume offers a unique and accessible overview of the most active fields in Stochastic Geometry, up to the frontiers of recent research. Since 2014, the yearly meeting of the French research structure GDR GeoSto has been preceded by two introductory courses. This book contains five of these introductory lectures. The first chapter is a historically motivated introduction to Stochastic Geometry which relates four classical problems (the Buffon needle problem, the Bertrand paradox, the Sylvester four-point problem and the bicycle wheel problem) to current topics. The remaining chapters give an application motivated introduction to contemporary Stochastic Geometry, each one devoted to a particular branch of the subject: understanding spatial point patterns through intensity and conditional intensities; stochastic methods for image analysis; random fields and scale invariance; and the theory of Gibbs point processes. Exposing readers to a rich theory, this book will encourage further exploration of the subject and its wide applications.
Stochastic Geometry: Likelihood and Computation (Chapman And Hall/crc Monographs On Statistics And Applied Probability Ser. #80)
by Wilfrid S. KendallStochastic geometry involves the study of random geometric structures, and blends geometric, probabilistic, and statistical methods to provide powerful techniques for modeling and analysis. Recent developments in computational statistical analysis, particularly Markov chain Monte Carlo, have enormously extended the range of feasible applications. Stochastic Geometry: Likelihood and Computation provides a coordinated collection of chapters on important aspects of the rapidly developing field of stochastic geometry, including: o a "crash-course" introduction to key stochastic geometry themeso considerations of geometric sampling bias issueso tesselationso shapeo random setso image analysiso spectacular advances in likelihood-based inference now available to stochastic geometry through the techniques of Markov chain Monte Carlo
Stochastic Geometry Analysis of Cellular Networks
by Martin Haenggi Bartłomiej Błaszczyszyn Paul Keeler Sayandev MukherjeeAchieve faster and more efficient network design and optimization with this comprehensive guide. Some of the most prominent researchers in the field explain the very latest analytic techniques and results from stochastic geometry for modeling the signal-to-interference-plus-noise ratio (SINR) distribution in heterogeneous cellular networks. This book will help you understand the effects of combining different system deployment parameters on such key performance indicators as coverage and capacity, enabling efficient allocation of simulation resources. In addition to covering results for network models based on the Poisson point process, this book presents recent results for when non-Poisson base station configurations appear Poisson due to random propagation effects such as fading and shadowing, as well as non-Poisson models for base station configurations, with a focus on determinantal point processes and tractable approximation methods. Theoretical results are illustrated with practical long-term evolution (LTE) applications and compared with real-world deployment results.