An Introduction to Stochastic Modeling - Hardcover

Mark A. Pinsky; Samuel Karlin

Hardcover

ISBN 10: 0123814162 ISBN 13: 9780123814166

Publisher: Academic Press, 2010

Synopsis

Serving as the foundation for a one-semester course in stochastic processes for students familiar with elementary probability theory and calculus, Introduction to Stochastic Modeling, Fourth Edition, bridges the gap between basic probability and an intermediate level course in stochastic processes. The objectives of the text are to introduce students to the standard concepts and methods of stochastic modeling, to illustrate the rich diversity of applications of stochastic processes in the applied sciences, and to provide exercises in the application of simple stochastic analysis to realistic problems.

New to this edition:

• Realistic applications from a variety of disciplines integrated throughout the text, including more biological applications
• Plentiful, completely updated problems
• Completely updated and reorganized end-of-chapter exercise sets, 250 exercises with answers
• New chapters of stochastic differential equations and Brownian motion and related processes
• Additional sections on Martingale and Poisson process

• Realistic applications from a variety of disciplines integrated throughout the text
• Extensive end of chapter exercises sets, 250 with answers
• Chapter 1-9 of the new edition are identical to the previous edition
• New! Chapter 10 - Random Evolutions
• New! Chapter 11- Characteristic functions and Their Applications

About this title

Review

Serving as the foundation for a one-semester course in stochastic processes for students familiar with elementary probability theory and calculus, the fourth edition of Introduction to Stochastic Modeling bridges the gap between basic probability and an intermediate level course in stochastic processes. The objectives of the text are to introduce students to the standard concepts and methods of stochastic modeling, to illustrate the rich diversity of applications of stochastic processes in the applied sciences, and to provide exercises in the application of simple stochastic analysis to realistic problems.

About This Edition

In the fourth edition, we have added two new chapters: Chapter 10 on random evolution and Chapter 11 on characteristic functions. Chapter 10, "Random Evolution," denotes a set of stochastic models, which describe continuous motion with piecewise linear sample functions. Explicit formulas are available in the simplest cases. In the general case, one has a central limit theorem, which is pursued more generally in Chapter 11, “Characteristic Functions and Their Applications.” Here the necessary tools from Fourier analysis are developed and applied when necessary. Many theorems are proved in full detail, while other proofs are sketched--in the spirit of the earlier Chapters 1-9. Complete proofs may be found by consulting the intermediate textbooks listed in the section on further reading. Instructors who have taught from the third edition may be reassured that Chapters 1-9 of the new edition are identical to the corresponding chapters of the new book.

Changes This Edition

• Realistic applications from a variety of disciplines integrated throughout the text, including more biological applications
• Plentiful, completely updated problems
• Completely updated and reorganized end-of-chapter exercise sets, 250 exercises with answers
• New chapters of stochastic differential equations and Brownian motion and related processes
• Additional sections on Martingale and Poisson process

Read a sample chapter from Introduction to Stochastic Modeling.

Review

PRAISE FOR THE SECOND EDITION "This book is a valuable resource for anyone studying combustion processes." --David L. Liscinsky, United Technologist Research Center, in AIAA JOURNAL

"This is an excellent text-book ... The narrative is clear, careful and detailed but, at the same time, designed to draw (not to bore) the reader in. The main strengths, in my opinion, are the wealth of convincing applications, which are discussed at some, but not too much length after each bit of theoretical development, and the large number of exercises given at the ends of sections, not just at the ends of chapters." --Martin Crowder, University of Surrey, Guildford, in THE STATISTICIAN

Edition details

• Publisher: Academic Press
• Publication date: 2010
• Language: English
• ISBN 10: 0123814162
• ISBN 13: 9780123814166
• Binding: Hardcover
• Edition number: 4
• Number of pages: 584