Springer Series in Statistics

An Introduction to Stochastic Processes and Their Applications

Authors: Todorovic, Petar

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About this book

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 (1 chapter)

  • Markov Processes I

    Petar Todorovic

    Pages 200-231

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Buy this book

eBook $89.99 net
( price for USA )
  • ISBN 978-1-4613-9742-7
  • digitally watermarked, no DRM
  • included format: PDF
  • eBooks can be used on all Reading Devices
Softcover $119.00 net
( price for USA )
  • ISBN 978-1-4613-9744-1
  • free shipping for individuals worldwide
  • usually dispatched within 3 to 5 business days

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Bibliographic Information

Bibliographic Information
Book Title
An Introduction to Stochastic Processes and Their Applications
Series Title
Springer Series in Statistics
Copyright
1992
Publisher
Springer-Verlag New York
Copyright Holder
The Applied Probability Trust
eBook ISBN
978-1-4613-9742-7
DOI
10.1007/978-1-4613-9742-7
Softcover ISBN
978-1-4613-9744-1
Series ISSN
0172-7397
Edition Number
1
Topics