MARK PINSKY, SAMUEL KARLIN – AN INTRODUCTION TO STOCHASTIC MODELING 4TH ED

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AMAZON.COM REVIEW

The fourth edition serves as the foundation for a one-semester course in stochastic processes for students who are familiar with elementary probability theory. There is an introduction to Stochastic Modeling. There is a gap between basic probability and an intermediate level course. To demonstrate 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 are some of the objectives of the text.

ABOUT THIS EDITION

Chapter 10 on random evolution and Chapter 11 on characteristic functions were added in the fourth edition. Chapter 10 refers to a set of models that describe continuous motion with piecewise linear sample functions. In the simplest cases, explicit formulas are available. In the general case, one has a central limit theorem, which is pursued more generally in Chapter 11, Characteristic Functions and Their Applications. The necessary tools are developed here. In the spirit of the earlier Chapters 1-9, many theorems are proved in full detail. It is possible to find complete proof by consulting the intermediate textbooks listed in the section. Instructors who have taught from the third edition may be reassured that Chapters 1-9 of the new edition are the same as the chapters in 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

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

The narrative is clear, careful and detailed but, at the same time, designed to draw the reader in. The main strengths, in my opinion, are the wealth of convincing applications, which are discussed at some, but not too long after each bit of theoretical development, and the large number of exercises given at the end of sections, not just at the ends of chapters.

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