Probability Theory

1. Front Matter

   Pages i-xiv

   PDF

2. Introduction

   • Vivek S. Borkar

   Pages 1-17

3. Spaces of Probability Measures

   • Vivek S. Borkar

   Pages 19-36

4. Conditioning and Martingales

   • Vivek S. Borkar

   Pages 37-63

5. Basic Limit Theorems

   • Vivek S. Borkar

   Pages 65-87

6. Markov Chains

   • Vivek S. Borkar

   Pages 89-108

7. Foundations of Continuous-Time Processes

   • Vivek S. Borkar

   Pages 109-129

8. Back Matter

   Pages 131-139

   PDF

This book presents a selection of topics from probability theory. Essentially, the topics chosen are those that are likely to be the most useful to someone planning to pursue research in the modern theory of stochastic processes. The prospective reader is assumed to have good mathematical maturity. In particular, he should have prior exposure to basic probability theory at the level of, say, K.L. Chung's 'Elementary probability theory with stochastic processes' (Springer-Verlag, 1974) and real and functional analysis at the level of Royden's 'Real analysis' (Macmillan, 1968). The first chapter is a rapid overview of the basics. Each subsequent chapter deals with a separate topic in detail. There is clearly some selection involved and therefore many omissions, but that cannot be helped in a book of this size. The style is deliberately terse to enforce active learning. Thus several tidbits of deduction are left to the reader as labelled exercises in the main text of each chapter. In addition, there are supplementary exercises at the end. In the preface to his classic text on probability ('Probability', Addison­ Wesley, 1968), Leo Breiman speaks of the right and left hands of probability.

• Markov chain
• Markov property
• Martingale
• Operations Research
• Probability theory
• Random variable
• Stochastic processes
• Uniform integrability
• stochastic process

• Department of Electrical Engineering, Indian Institute of Science, Bangalore, India

  Vivek S. Borkar

Policies and ethics