Probability: Theory and Examples
by Rick Durrett
Publisher: Cambridge University Press 2010
Number of pages: 372
This book is an introduction to probability theory covering laws of large numbers, central limit theorems, random walks, martingales, Markov chains, ergodic theorems, and Brownian motion. It is a comprehensive treatment concentrating on the results that are the most useful for applications. Its philosophy is that the best way to learn probability is to see it in action.
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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 ...
by Robert B. Ash - Dover Publications
This text surveys random variables, conditional probability and expectation, characteristic functions, infinite sequences of random variables, Markov chains, and an introduction to statistics. Geared toward advanced undergraduates and graduates.
by Douglas Kennedy - Trinity College
This material was made available for the course Probability of the Mathematical Tripos. Contents: Basic Concepts; Axiomatic Probability; Discrete Random Variables; Continuous Random Variables; Inequalities, Limit Theorems and Geometric Probability.
by Marek Biskup - arXiv
Recent progress on understanding of the Random Conductance Model is reviewed and commented. A particular emphasis is on the results on the scaling limit of the random walk among random conductances for almost every realization of the environment.