Stochastic Programing

Writing for graduate students dealing with stochastic processes in a range of fields (such as operations research, management science, engineering, computer science, applied mathematics, and economics

Collects the 30 lectures delivered during the July 1999 NATO advanced study institute on the rules, theorems, models, and applications of stochastic games. The longest paper proves the existence of s

This book presents a thorough development of the modern theory of stochastic approximation or recursive stochastic algorithms for both constrained and unconstrained problems. This second edition is a

This textbook has been developed from the lecture notes for a one-semester course on stochastic modelling. It reviews the basics of probability theory and then covers the following topics: Markov chai

This textbook has been developed from the lecture notes for a one-semester course on stochastic modelling. It reviews the basics of probability theory and then covers the following topics: Markov chai

Today's modern network traffic, which is distinctly different from traditional voice traffic, generates challenging mathematical and statistical problems. Stochastic Modeling in Broadband Communicatio

This work focuses on analyzing and presenting solutions for a wide range of stochastic problems that are encountered in applied mathematics, probability, physics, engineering, finance, and economics.

This book presents the recent development of stochastic approximation algorithms with expanding truncations based on the TS (trajectory-subsequence) method, a newly developed method for convergence an

Emphasizing the foundations of dynamic optimization models, this book presents foundational results, concepts, methods, and tools useful in building and analyzing stochastic inventory models. Topics

Stochastic processes with jumps and random measures are importance as drivers in applications like financial mathematics and signal processing. This 2002 text develops stochastic integration theory for both integrators (semimartingales) and random measures from a common point of view. Using some novel predictable controlling devices, the author furnishes the theory of stochastic differential equations driven by them, as well as their stability and numerical approximation theories. Highlights feature DCT and Egoroff's Theorem, as well as comprehensive analogs results from ordinary integration theory, for instance previsible envelopes and an algorithm computing stochastic integrals of càglàd integrands pathwise. Full proofs are given for all results, and motivation is stressed throughout. A large appendix contains most of the analysis that readers will need as a prerequisite. This will be an invaluable reference for graduate students and researchers in mathematics, physics, electrical en

This book presents the general theory and basic methods of linear and nonlinear stochastic systems (StS). It outlines StS structural theory, including direct numerical methods, methods of normalizatio

A collection of articles written by mathematicians and physicists, designed to describe the state of the art in climate models with stochastic input. Mathematicians will benefit from a survey of simpl

Situated between the very large Rational Unified Process and the very small eXtreme programing approach, the ICONIX process makes use of the Unified Modeling Language. The authors overview this proces

The first complete guide to using the Stochastic Finite Element Method for reliability assessmentUnlike other analytical reliability estimation techniques, the Stochastic Finite Element Method (SFEM)

A breakthrough approach to the theory and applications of stochastic integration The theory of stochastic integration has become an intensely studied topic in recent years, owing to its extraordinaril

A profound look at the origins of patient's maladies and the way they lead their lives. The author describes the analyses leading to de-programing these patients from their toxins and intoxicators. Th

Ideal for courses aiming to give examples of the wide variety of empirical phenomena for which stochastic processes provide mathematical models. It introduces the methods of probability model building

Beginning with Jackson networks and ending with spatial queuing systems, this book describes several basic stochastic network processes, with the focus on network processes that have tractable express

A text for a graduate engineering course, explaining how to apply discrete stochastic processes to problems in engineering and operations research. Focusing on application, presents many simple exampl

Focusing on the mathematical description of stochastic dynamics in discrete as well as in continuous time, this book investigates such dynamical phenomena as perturbations, bifurcations and chaos. It

Stochastic Processes for Insurance and Finance offers a thorough yet accessible reference for researchers and practitioners of insurance mathematics. Building on recent and rapid developments in appli

This book describes the stochastic method for ocean wave analysis. This method provides a route to predicting the characteristics of random ocean waves - information vital for the design and safe operation of ships and ocean structures. Assuming a basic knowledge of probability theory, the book begins with a chapter describing the essential elements of wind-generated random seas from the stochastic point of view. The following three chapters introduce spectral analysis techniques, probabilistic predictions of wave amplitudes, wave height and periodicity. A further four chapters discuss sea severity, extreme sea state, the directional wave energy spreading in random seas and special wave events such as wave breaking and group phenomena. Finally the stochastic properties of non-Gaussian waves are presented. Useful appendices and an extensive reference list are included. Examples of practical applications of the theories presented can be found throughout the text. This book will be suitab

This monograph is intended to give atmospheric scientists a basic understanding of the physical and mathematical foundations of stochastic Lagrangian models of turbulent diffusion.

An introductory text pinpointing the stochastic theories useful for application to mathematical finance, queuing, biology, and physics. Durrett (mathematics, Cornell U.) describes Brownian motion and

This book summarizes developments related to a class of methods called Stochastic Decomposition (SD) algorithms, which represent an important shift in the design of optimization algorithms. Unlike tra

This volume considers the regularity theory of solutions to stochastic differential equations, and the existence of stochastic flows, Regularity properties are one of the main tools for the analysis o

A nonmeasure theoretic introduction to stochastic processes. Considers its diverse range of applications and provides readers with probabilistic intuition and insight in thinking about problems. This

Durham Symposia traditionally constitute an excellent survey of recent developments in many areas of mathematics. The Symposium on stochastic analysis, which took place at the University of Durham in July 1990, was no exception. This volume is edited by the organizers of the Symposium, and contains papers contributed by leading specialists in diverse areas of probability theory and stochastic processes. Of particular note are the papers by David Aldous, Harry Kesten and Alain-Sol Sznitman, all of which are based upon short courses of invited lectures. Researchers into the varied facets of stochastic analysis will find that these proceedings are an essential purchase.

The theory of stochastic processes has developed so much in the last twenty years that the need for a systematic account of the subject has been felt, particularly by students and instructors of proba

Stochastic games have an element of chance: the state of the next round is determined probabilistically depending upon players' actions and the current state. Successful players need to balance the need for short-term payoffs while ensuring future opportunities remain high. The various techniques needed to analyze these often highly non-trivial games are a showcase of attractive mathematics, including methods from probability, differential equations, algebra, and combinatorics. This book presents a course on the theory of stochastic games going from the basics through to topics of modern research, focusing on conceptual clarity over complete generality. Each of its chapters introduces a new mathematical tool – including contracting mappings, semi-algebraic sets, infinite orbits, and Ramsey's theorem, among others – before discussing the game-theoretic results they can be used to obtain. The author assumes no more than a basic undergraduate curriculum and illustrates the theory with num

Stochastic processes occur everywhere in sciences and engineering, and need to be understood by applied mathematicians, engineers and scientists alike. This book introduces the reader gently to the su

The relatively young theory of structured dependence between stochastic processes has many real-life applications in areas including finance, insurance, seismology, neuroscience, and genetics. With this monograph, the first to be devoted to the modeling of structured dependence between random processes, the authors not only meet the demand for a solid theoretical account but also develop a stochastic processes counterpart of the classical copula theory that exists for finite-dimensional random variables. Presenting both the technical aspects and the applications of the theory, this is a valuable reference for researchers and practitioners in the field, as well as for graduate students in pure and applied mathematics programs. Numerous theoretical examples are included, alongside examples of both current and potential applications, aimed at helping those who need to model structured dependence between dynamic random phenomena.

A vigorous response to the challenges of incorporating computer use into the teaching and learning of stochastic processes, this book takes an applications- and computer-oriented approach rather than

This 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 stru

This book presents a unified framework for the tractable analysis of large-scale, multi-antenna wireless networks using stochastic geometry. This mathematical analysis is essential for assessing and u

The book covers control and filtering problems for several classes of stochastic networked systems including stability, robustness, reliability, consensus performance, and/or disturbance attenuation l

Emilia Graß develops a solution method which can provide fast and near-optimal solutions to realistic large-scale two-stage stochastic problems in disaster management. The author proposes a specialize

This book aims to provide a unified treatment on the analysis and synthesis for discrete-time stochastic systems with guarantee of certain performances against network-enhanced complexities with appli

This textbook shall serve a double purpose: first of all, it is a book about generalized stochastic processes, a very important but highly neglected part of probability theory which plays an outstandi

The YUIMA package is the first comprehensive R framework based on S4 classes and methods which allows for the simulation of stochastic differential equations driven by Wiener process, Lévy processes o