Lectures on Stochastic Analysis: Diffusion Theory

Daniel W. Stroock

doi:10.1017/CBO9780511623752

This book is based on a course given at Massachusetts Institute of Technology. It is intended to be a reasonably self-contained introduction to stochastic analytic techniques that can be used in the study of certain problems. The central theme is the theory of diffusions. In order to emphasize the intuitive aspects of probabilistic techniques, diffusion theory is presented as a natural generalization of the flow generated by a vector field. Essential to the development of this idea is the introduction of martingales and the formulation of diffusion theory in terms of martingales. The book will make valuable reading for advanced students in probability theory and analysis and will be welcomed as a concise account of the subject by research workers in these fields.

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Lectures on Stochastic Analysis: Diffusion Theory

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Contents

Frontmatter
pp i-iv

Contents
pp v-vi

Introduction
pp vii-x

1 - Stochastic processes and measures on function space
pp 1-18

2 - Diffusions and martingales
pp 19-72

3 - The martingale problem formulation of diffusion theory
pp 73-119

Appendix
pp 120-126

Index
pp 127-128

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Lectures on Stochastic Analysis: Diffusion Theory

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