Probability, Random Processes, and Ergodic Properties
by Robert M. Gray
Publisher: Springer 2008
Number of pages: 217
This book is a self-contained treatment of the theory of probability, random processes. It is intended to lay solid theoretical foundations for advanced probability, that is, for measure and integration theory, and to develop in depth the long term time average behavior of measurements made on random processes with general output alphabets.
Home page url
Download or read it online for free here:
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 H.R. Pitt - Tata institute of Fundamental Research
Measure Theory (Sets and operations on sets, Classical Lebesgue and Stieltjes measures, Lebesgue integral); Probability (Function of a random variable, Conditional probabilities, Central Limit Problem, Random Sequences and Convergence Properties).
by Davar Khoshnevisan, Firas Rassoul-Agha - University of Utah
This is a first course in undergraduate probability. It covers standard material such as combinatorial problems, random variables, distributions, independence, conditional probability, expected value and moments, law of large numbers, etc.
by Cosma Rohilla Shalizi - Carnegie Mellon University
Text for a second course in stochastic processes. It is assumed that you have had a first course on stochastic processes, using elementary probability theory. You will study stochastic processes within the framework of measure-theoretic probability.