Brownian Motion, Martingales, and Stochastic Calculus [book]

Jean-François Le Gall
2013 Zenodo  
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
more » ... owledge 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
doi:10.5281/zenodo.4461774 fatcat:jojrvw2osbbwzkxwjk4bvuwqaq