Some Topics in Probability and Analysis

Résumé du livre

This book is based on lectures presented by the author at DePaul University in July 1986. The lectures cover three main topics. The first is local time theory for Brownian motion and some geometrical inequalities for harmonic functions in the upper half-plane R^{n+1}_+. The author sketches a proof of the inequalities obtained by Barlow and Yor for the maximal local time functional. The second topic concerns a probabilistic treatment of Riesz transforms in R^{n+1}_+, and semimartingale inequalities. The author proves semimartingale inequalities of the type usually obtained for martingales. The.