Mathematical Foundations of Probability Theory
by Gane Samb Lo
Publisher: arXiv.org 2018
Number of pages: 378
The fundamental aspects of Probability Theory are presented from a pure mathematical view based on Measure Theory. Such an approach places Probability Theory in its natural frame of Functional Analysis and constitutes a firm preparation to the study of Random Analysis and Stochastic processes.
Home page url
Download or read it online for free here:
by David Nualart - The University of Kansas
From the table of contents: Stochastic Processes (Probability Spaces and Random Variables, Definitions and Examples); Jump Processes (The Poisson Process, Superposition of Poisson Processes); Markov Chains; Martingales; Stochastic Calculus.
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 John Maynard Keynes - Macmillan and co
From the table of contents: Fundamental ideas - The Meaning of Probability, The Measurement of Probabilities; Fundamental theorems; Induction and analogy; Some philosophical applications of probability; The foundations of statistical inference, etc.
by Gian-Carlo Rota - David Ellerman
In 1999, Gian-Carlo Rota gave his famous course, Probability, at MIT for the last time. The late John N. Guidi taped the lectures and took notes which he then wrote up in a verbatim manner conveying the substance and the atmosphere of the course.