Stochastic Programing

This book focuses on optimization problems involving uncertain parameters and covers the theoretical foundations and recent advances in areas where stochastic models are available. It will be useful t

Stochastic optimization problems arise in decision-making problems under uncertainty, and find various applications in economics and finance. On the other hand, problems in finance have recently led t

Permutation testing for multivariate stochastic ordering and ANOVA designs is a fundamental issue in many scientific fields such as medicine, biology, pharmaceutical studies, engineering, economics,

This volume presents an introductory course on differential stochastic equations and Malliavin calculus.The material of the book has grown from a series of courses delivered at the Scuola Normale Supe

In the third edition of this classic the chapter on quantum Marcov processes has been replaced by a chapter on numerical treatment of stochastic differential equations to make the book even more valua

In May 2006, The University of Utah hosted an NSF-funded minicourse on stochastic partial differential equations. The goal of this minicourse was to introduce graduate students and recent Ph.D.s to va

The book gives an overview of path integral quantization and stochastic quantization of classical mechanics and field theory. The non-Abelian gauge field, the gravitational field, and the path integra

Based on lectures given by one of the authors with many years of experience in teaching stochastic processes, this textbook is unique in combining basic mathematical and physical theory with numerous

This book presents a stochastic management approach for manufacturing and service enterprises with risks by a game/strategic view in order to show the goal and constraints on these enterprises and to

This simple, compact toolkit for designing and analyzing stochastic approximation algorithms requires only basic literacy in probability and differential equations. Yet these algorithms have powerful applications in control and communications engineering, artificial intelligence and economic modelling. The dynamical systems viewpoint treats an algorithm as a noisy discretization of a limiting differential equation and argues that, under reasonable hypotheses, it tracks the asymptotic behaviour of the differential equation with probability one. The differential equation, which can usually be obtained by inspection, is easier to analyze. Novel topics include finite-time behaviour, multiple timescales and asynchronous implementation. There is a useful taxonomy of applications, with concrete examples from engineering and economics. Notably it covers variants of stochastic gradient-based optimization schemes, fixed-point solvers, which are commonplace in learning algorithms for approximate

This book covers a highly relevant and timely topic that is of wide interest, especially in finance, engineering and computational biology. The introductory material on simulation and stochastic diffe

The 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. Appendice

For most cases of interest, exact solutions to nonlinear equations describing stochastic dynamical systems are not available. This book details the relatively simple and popular linearization techniqu

This volume examines the theory of fractional Brownian motion and other long-memory processes. Interesting topics for PhD students and specialists in probability theory, stochastic analysis and financ

This research monograph develops the Hamilton-Jacobi-Bellman theory via dynamic programming principle for a class of optimal control problems for stochastic hereditary differential equations (SHDEs)

Since the publication of the first edition of this book, the area of mathematical finance has grown rapidly, with financial analysts using more sophisticated mathematical concepts, such as stochastic

This self-contained, practical, entry-level text integrates the basic principles of applied mathematics, applied probability, and computational science in a presentation of stochastic processes and co

This volume highlights recent developments of stochastic analysis with a wide spectrum of applications, including stochastic differential equations, stochastic geometry, and nonlinear partial differen

Stochastic discrete-event systems (SDES) capture the randomness in choices due to activity delays and the probabilities of decisions. This book delivers a comprehensive overview on modeling with a qua

These lectures concentrate on (nonlinear) stochastic partial differential equations (SPDE) of evolutionary type. There are three approaches to analyze SPDE: the "martingale measure approach", the "mil

This work presents the theory of stochastic processes in its present state of rich imperfection. It is more than an encyclopedic work. Some parts read like a textbook, but others are more technical an

This book deals with collective and stochastic processes in astrophysical disks involving theory, observations, and the results of modelling. It examines the spiral-vortex structure in galactic and ac

This book presents a self-contained introduction to stochastic processes with emphasis on their applications in science, engineering, finance, computer science, and operations research. It provides th

Incorporates the many tools needed for modeling and pricing in finance and insurance Introductory Stochastic Analysis for Finance and Insurance introduces readers to the topics needed to master and u

This is a book on stochastic dynamic macroeconomics from a Keynesian perspective. It shows that including Keynesian features in intertemporal models considerably contributes to resolve major puzzles

Stochastic numerical methods play an important role in large scale computations in the applied sciences. The first goal of this book is to give a mathematical description of classical direct simulatio

This text is designed both for students of probability and stochastic processes, and for students of functional analysis. For the reader not familiar with functional analysis a detailed introduction to necessary notions and facts is provided. However, this is not a straight textbook in functional analysis; rather, it presents some chosen parts of functional analysis that can help understand ideas from probability and stochastic processes. The subjects range from basic Hilbert and Banach spaces, through weak topologies and Banach algebras, to the theory of semigroups of bounded linear operators. Numerous standard and non-standard examples and exercises make the book suitable as a course textbook or for self-study.

This text is designed both for students of probability and stochastic processes, and for students of functional analysis. For the reader not familiar with functional analysis a detailed introduction to necessary notions and facts is provided. However, this is not a straight textbook in functional analysis; rather, it presents some chosen parts of functional analysis that can help understand ideas from probability and stochastic processes. The subjects range from basic Hilbert and Banach spaces, through weak topologies and Banach algebras, to the theory of semigroups of bounded linear operators. Numerous standard and non-standard examples and exercises make the book suitable as a course textbook or for self-study.

The interplay between functional and stochastic analysis has wide implications for problems in partial differential equations, noncommutative or "free" probability, and Riemannian geometry. Written by

The problem of stochastic control of partially observable systems plays an important role in many applications. All real problems are in fact of this type, and deterministic control as well as stochastic control with full observation can only be approximations to the real world. This justifies the importance of having a theory as complete as possible, which can be used for numerical implementation. This book first presents those problems under the linear theory that may be dealt with algebraically. Later chapters discuss the nonlinear filtering theory, in which the statistics are infinite dimensional and thus, approximations and perturbation methods are developed.

It is with great pleasure that we present to you this tutorial volume entitled Validation of Stochastic Systems.ItisoneoftheresultsoftheDutch-German- lateral cooperation project “Validation of Stochas

This book contains 18 articles on stochastic processes (stochastic calculus and Malliavin calculus, functionals of Brownian motions and Levy processes, stochastic control and optimization problems, st

Stochastic Calculus for Finance evolved from the first ten years of the Carnegie Mellon Professional Master's program in Computational Finance. The content of this book has been used successfully wit

This accessible introduction to the theory of stochastic processes emphasizes Levy processes and Markov processes. It gives a thorough treatment of the decomposition of paths of processes with indepen

This volume provides a general field-theoretical picture of critical phenomena and stochastic dynamics and helps readers develop a practical skill for calculations. This education on the practical ski

Limit theorems for stochastic processes are an important part of probability theory and mathematical statistics and one model that has attracted the attention of many researchers working in the area i

It has been 15 years since the first edition of Stochastic Integration and Differential Equations, A New Approach appeared, and in those years many other texts on the same subject have been published,

Lande (biology, U. of California, San Diego) introduces biological concepts and mathematical methods that have proven useful in analyzing stochastic population dynamics, using field data from bird, ma

The contributions in this volume highlight emergent research in the area of stochastic analysis and mathematical physics, focussing, in particular, on quantum probability. Key topics covered include n

This volume by two international leaders in the field proposes a systematic exposition of convergence in law for stochastic processes from the point of view of semimartingale theory. It emphasizes res