About the BookAbout the AuthorTable of Contents

This book covers the basics of modern probability theory. It begins with probability theory on finite and countable sample spaces and then passes from there to a concise course on measure theory, which is followed by some initial applications to probability theory, including independence and conditional expectations. The second half of the book deals with Gaussian random variables, with Markov chains, with a few continuous parameter processes, including Brownian motion, and, finally, with martingales, both discrete and continuous parameter ones. The book is a self-contained introduction to probability theory and the measure theory required to study it.

Daniel W. Stroock, Massachusetts Institute of Technology, Cambridge, MA

• Title page 2
• Contents 4
• Preface 10
• Some background and preliminaries 14
• Probability theory on uncountable sample spaces 68
• Some applications to probability theory 118
• The central limit theorem and Gaussian distributions 148
• Discrete parameter stochastic processes 172
• Some continuous-time processes 206
• Martingales 238
• Notation 288
• Bibliography 292
• Index 294