Advanced Topics in Probability
by S.R.S. Varadhan
Publisher: New York University 2011
Number of pages: 203
Topics: Brownian Motion; Continuous Parameter Martingales; Diffusion Processes; Weak convergence and Compactness; Stochastic Integrals and Ito's formula; Markov Processes, Kolmogorov's equations; Stochastic Differential Equations; Existence and Uniqueness; Girsanov Formula; Random Time Change; The two dimensional case; The General Case; Limit Theorems; Reflected Brownian Motion; Reflection in higher dimensions; Invariant Measures.
Download or read it online for free here:
(multiple PDF files)
by William G. Faris - University of Arizona
From the table of contents: Combinatorics; Probability Axioms; Discrete Random Variables; The Bernoulli Process; Continuous Random Variables; The Poisson Process; The weak law of large numbers; The central limit theorem; Estimation.
by Vladislav Kargin - arXiv
Contents: Non-commutative Probability Spaces; Distributions; Freeness; Asymptotic Freeness of Random Matrices; Asymptotic Freeness of Haar Unitary Matrices; Free Products of Probability Spaces; Law of Addition; Limit Theorems; Multivariate CLT; etc.
by Peter G. Doyle, J. Laurie Snell - Dartmouth College
In this work we will look at the interplay of physics and mathematics in terms of an example where the mathematics involved is at the college level. The example is the relation between elementary electric network theory and random walks.
by Gane Samb Lo - arXiv.org
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 offers a basis towards Statistics Theory.