ABSTRACT

This book will enable researchers and students of analysis to more easily understand research papers in which probabilistic methods are used to prove theorems of analysis, many of which have no other known proofs. The book assumes a course in measure and integration theory but requires little or no background in probability theory. It emplhasizes topics of interest to analysts, including random series, martingales and Brownian motion.

chapter Chapter 1|17 pages

Fourier Transforms on ℝ d

chapter Chapter 2|13 pages

Weak Convergence in M1(ℝ d )

chapter Chapter 3|23 pages

Independence

chapter Chapter 4|24 pages

Infinite Series of Random Vectors

chapter Chapter 5|48 pages

Normal Distributions and Central Limits

chapter Chapter 6|46 pages

Martingales

chapter Chapter 8|67 pages

Brownian Motions

chapter Chapter 9|20 pages

Random Fourier Series of Continuous Functions

chapter Chapter 10|9 pages

Fourier Coefficients of Continuous Functions