Stochastic Processes (Courant Lecture Notes) by S. R. S. Varadhan (PDF)

Description

This is a brief introduction to stochastic processes studying certain elementary continuous-time processes. After a description of the Poisson process and related processes with independent increments as well as a brief look at Markov processes with a finite number of jumps, the author proceeds to introduce Brownian motion and to develop stochastic integrals and Itô’s theory in the context of one-dimensional diffusion processes. The book ends with a brief survey of the general theory of Markov processes. The book is based on courses given by the author at the Courant Institute and can be used as a sequel to the author’s successful book Probability Theory in this series. Titles in this series are co-published with the Courant Institute of Mathematical Sciences at New York University.

User’s Reviews

Editorial Reviews: Review Amazingly, almost all of the proofs are given explicitly. In fact the author provides only eight references in the bibliography. This reflects the fact that, as a whole, this book is written in a totally self-contained manner. …I can say that this book is a set of very well-written lecture notes, and it is organized as a clear synthesis of the theory of continuous-time stochastic processes with many examples and with plenty of exercises…” –Mathematical ReviewsThe text is one of those that may be strongly recommended to all young mathematicians as a starter to precede a deeper study of probability and stochastic processes. –EMS Newsletter

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Very nice notes. This is very readable than other rigorous textbooks. I think this book is the best choice for review.

⭐This book is a follow up of the author’s text “Probability Theory”. Stochastic processes/differential equations appear in numerous physical phenomena and applications including finance. The book covers all the topics a graduate student in probability or even an aspiring analyst would need to learn. Connections to parabolic partial differential equations are also discussed. This text is meant to be introductory and yet does a good job of leading a reader through the main ideas and important theorems. Exercises are also plentyful and are a must for any one trying to learn this material. They highlight and often expand on the important ideas used in proofs. However, in order to get the most out of this and “Probability Theory”, one should first learn real analysis with measure theory before taking on these texts. Incidentally, the author is a world expert on these matters, having also won the Abel prize recently.I recommend highly both texts. I have given it four stars(=excellent).

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