Stochastic Calculus

Applications in Science and Engineering

AvMircea Grigoriu

Inbunden, Engelska, 2002

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Beskrivning

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. The approach used reduces the gap between the mathematical and engineering literature. Stochastic problems are defined by algebraic, differential or integral equations with random coefficients and/or input. However, it is the type, rather than the particular field of application, that is used to categorize these problems. An introductory chapter outlines the types of stochastic problems under consideration in this book and illustrates some of their applications. A user-friendly, systematic exposition unfolds as follows: the essentials of probability theory, random processes, stochastic integration, and Monte Carlo simulation are developed in chapters two to five. The Monte Carlo method is used extensively to illustrate difficult theoretical concepts and solve numerically some of the stochastic problems in chapters six to nine.

Produktinformation

Utgivningsdatum:2002-09-24
Mått:156 x 234 x 48 mm
Vikt:1 338 g
Format:Inbunden
Språk:Engelska
Antal sidor:775
Upplaga:2002
Förlag:Birkhauser Boston
ISBN:9780817642426

Utforska kategorier

Tillämpad matematik inom Naturvetenskap och teknik

Recensioner i media

"When familiar at least with the basics of measure theoretic probability, one may use this book to get a feel for the type of problems one tackles with the given methods and the type of results one can expect and then proceed to more detailed expositions... The book is an impressive achievement." -Mathematical Reviews "The large number of examples...as well as the good survey on advanced mathematical techniques make the textbook very valuable for people working in mathematics with a view towards applications... The applications range from climate dynamics over material sciences and mechanics to pattern formation, physics and finance. The presentation is very successful in providing a sound mathematical background without getting lost in too much technical detail. Most results are proved completely, for the others the main ideas and intuition are given and references for detailed expositions are given... At the end of each chapter a list of instructive exercises is provided. The long list of references covers theoretical mathematical works as well as highly applied areas. Altogether this textbook has all the necessary prerequisites for boosting the interdisciplinary collaboration between applied scientists and probabilists." -Zentralblatt Math "This is an impressive compendium, which, on its first 280 pages, provides a quite thorough review of probability theory, stochastic processes, Ito's formula and stochastic differential equations... Although the focus is on the mathematical theory, many examples from sciences or engineering illustrate the concepts and methods. Each chapter ends with a number of problems. This book will be of substantial interest to the applied scientists seeking methods to solve stochastic problems." -Monatshefte fur Mathematik

Innehållsförteckning

Introduction * Probability Theory * Stochastic Processes * Itô's Formula and Stochastic Differential Equations * Monte Carlo Simulation * Deterministic System and Input * Deterministic System and Stochastic Input * Stochastic System and Deterministic Input * Stochastic System and Stochastic Input * Bibliography * Index