Foundations of Constructive Probability Theory
by Yuen-Kwok Chan
Publisher: arXiv.org 2019
Number of pages: 517
We provide 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; and the input data, the construction procedure, and the output objects shall be regarded as integral parts of the theorem.
Home page url
Download or read it online for free here:
by S.R.S. Varadhan - New York University
Topics: Brownian Motion; 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; 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 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 Marcel B. Finan - Arkansas Tech University
This manuscript will help students prepare for the Probability Exam, the examination administered by the Society of Actuaries. This examination tests a student's knowledge of the fundamental probability tools for quantitatively assessing risk.