Radically Elementary Probability Theory
by Edward Nelson
Publisher: Princeton University Press 1987
Number of pages: 111
Nelson develops a new approach to probability theory that is just as powerful as but much simpler than conventional Kolmogorov-style probability theory used throughout mathematics for most of the 20th century.
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by Rick Durrett - Cambridge University Press
An introduction to probability theory covering laws of large numbers, central limit theorems, random walks, martingales, Markov chains, ergodic theorems, and Brownian motion. It concentrates on the results that are the most useful for applications.
by Remco van der Hofstad - Eindhoven University of Technology
These lecture notes are intended to be used for master courses, where the students have a limited prior knowledge of special topics in probability. We have included many of the preliminaries, such as convergence of random variables, etc.
by Yuen-Kwok Chan - arXiv.org
The author provides a systematic, thorough treatment of the foundations of probability theory and stochastic processes along the lines of E. Bishop's constructive analysis. Every existence result presented shall be a construction ...
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The three main themes of this book are probability theory, differential geometry, and the theory of integrable systems. The papers included here demonstrate a wide variety of techniques that have been developed to solve various mathematical problems.