# Introduction to Random Processes

• Yuriĭ A. Rozanov
Book

Part of the Springer Series in Soviet Mathematics book series (SSSOV)

## Table of contents

1. Front Matter
Pages I-VIII
2. Yuriĭ A. Rozanov
Pages 1-9
3. Yuriĭ A. Rozanov
Pages 10-17
4. Yuriĭ A. Rozanov
Pages 18-24
5. Yuriĭ A. Rozanov
Pages 25-32
6. Yuriĭ A. Rozanov
Pages 33-43
7. Yuriĭ A. Rozanov
Pages 44-51
8. Yuriĭ A. Rozanov
Pages 52-56
9. Yuriĭ A. Rozanov
Pages 57-60
10. Yuriĭ A. Rozanov
Pages 61-67
11. Yuriĭ A. Rozanov
Pages 68-72
12. Yuriĭ A. Rozanov
Pages 73-76
13. Yuriĭ A. Rozanov
Pages 77-83
14. Yuriĭ A. Rozanov
Pages 84-91
15. Yuriĭ A. Rozanov
Pages 92-99
16. Yuriĭ A. Rozanov
Pages 100-117
17. Back Matter
Pages 108-120

## About this book

### Introduction

Today, the theory of random processes represents a large field of mathematics with many different branches, and the task of choosing topics for a brief introduction to this theory is far from being simple. This introduction to the theory of random processes uses mathematical models that are simple, but have some importance for applications. We consider different processes, whose development in time depends on some random factors. The fundamental problem can be briefly circumscribed in the following way: given some relatively simple characteristics of a process, compute the probability of another event which may be very complicated; or estimate a random variable which is related to the behaviour of the process. The models that we consider are chosen in such a way that it is possible to discuss the different methods of the theory of random processes by referring to these models. The book starts with a treatment of homogeneous Markov processes with a countable number of states. The main topic is the ergodic theorem, the method of Kolmogorov's differential equations (Secs. 1-4) and the Brownian motion process, the connecting link being the transition from Kolmogorov's differential-difference equations for random walk to a limit diffusion equation (Sec. 5).

### Keywords

Brownian motion Markov process Random variable diffusion process ergodic theory filtration random walk stochastic differential equation

#### Authors and affiliations

• Yuriĭ A. Rozanov
• 1
1. 1.Steklov Mathematical InstituteMoscowUSSR

### Bibliographic information

• DOI https://doi.org/10.1007/978-3-642-72717-7
• Copyright Information Springer-Verlag Berlin Heidelberg 1987
• Publisher Name Springer, Berlin, Heidelberg
• eBook Packages
• Print ISBN 978-3-642-72719-1
• Online ISBN 978-3-642-72717-7
• Series Print ISSN 0939-1169
• About this book