by S. R. S. Varadhan
Publisher: New York University 2000
Number of pages: 300
These notes are based on a first year graduate course on Probability and Limit theorems given at Courant Institute of Mathematical Sciences. The text covers discrete time processes. A small amount of measure theory is included.
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by Michael Roeckner - Universitaet Bielefeld
From the table of contents: Introduction to Pathwise Ito-Calculus; (Semi-)Martingales and Stochastic Integration; Markov Processes and Semigroups - Application to Brownian Motion; Girsanov Transformation; Time Transformation.
by Russell Lyons, Yuval Peres - Cambridge University Press
This book is concerned with certain aspects of discrete probability on infinite graphs that are currently in vigorous development. Of course, finite graphs are analyzed as well, but usually with the aim of understanding infinite graphs and networks.
by Alexei Borodin, Vadim Gorin - arXiv
Topics include integrable models of random growth, determinantal point processes, Schur processes and Markov dynamics on them, Macdonald processes and their application to asymptotics of directed polymers in random media.
by Pierre Simon Laplace - Chapman & Hall
Classic book on probability theory. It demonstrates, without the use of higher mathematics, the application of probability to games of chance, physics, reliability of witnesses, astronomy, insurance, democratic government, and many other areas.