Book Open Access

Brownian Motion, Martingales, and Stochastic Calculus

Jean-François Le Gall

This book originates from lecture notes for an introductory course on stochastic calculus taught as part of the master’s program in probability and statistics at Université Pierre et Marie Curie and then at Université Paris-Sud. The aim of this course was to provide a concise but rigorous introduction to the theory of stochastic calculus for continuous semimartingales, putting a special emphasis on Brownian motion. This book is intended for students who already have a good knowledge of advanced probability theory, including tools of measure theory and the basic properties of conditional expectation. We also assume some familiarity with the notion of uniform integrability (see, for instance, Chapter VII in Grimmett and Stirzaker [30]). For the reader’s convenience, we record in Appendix A2 those results concerning discrete time martingales that we use in our study of continuous time martingales

Files (2.4 MB)
Name Size
2.4 MB Download
All versions This version
Views 2323
Downloads 164164
Data volume 400.8 MB400.8 MB
Unique views 2323
Unique downloads 160160


Cite as