An Introduction to Stochastic Processes and Their Applications

✍ Scribed by Petar Todorovic (auth.)

• Publisher: Springer-Verlag New York
• Year: 1992
• Tongue: English
• Leaves: 301
• Series: Springer Series in Statistics
• Edition: 1
• Category: Library

✦ Synopsis

This text on stochastic processes and their applications is based on a set of lectures given during the past several years at the University of California, Santa Barbara (UCSB). It is an introductory graduate course designed for classroom purposes. Its objective is to provide graduate students of statistics with an overview of some basic methods and techniques in the theory of stochastic processes. The only prerequisites are some rudiments of measure and integration theory and an intermediate course in probability theory. There are more than 50 examples and applications and 243 problems and complements which appear at the end of each chapter. The book consists of 10 chapters. Basic concepts and definitions are pro­ vided in Chapter 1. This chapter also contains a number of motivating ex­ amples and applications illustrating the practical use of the concepts. The last five sections are devoted to topics such as separability, continuity, and measurability of random processes, which are discussed in some detail. The concept of a simple point process on R+ is introduced in Chapter 2. Using the coupling inequality and Le Cam's lemma, it is shown that if its counting function is stochastically continuous and has independent increments, the point process is Poisson. When the counting function is Markovian, the sequence of arrival times is also a Markov process. Some related topics such as independent thinning and marked point processes are also discussed. In the final section, an application of these results to flood modeling is presented.

✦ Table of Contents

Front Matter....Pages i-xiii
Basic Concepts and Definitions....Pages 1-33
The Poisson Process and Its Ramifications....Pages 34-61
Elements of Brownian Motion....Pages 62-91
Gaussian Processes....Pages 92-105
L 2 Space....Pages 106-128
Second-Order Processes....Pages 129-149
Spectral Analysis of Stationary Processes....Pages 150-199
Markov Processes I....Pages 200-231
Markov Processes II: Application of Semigroup Theory....Pages 232-257
Discrete Parameter Martingales....Pages 258-278
Back Matter....Pages 279-290

✦ Subjects

Probability Theory and Stochastic Processes; Statistics, general