Some Topics in Probability and Analysis (Cbms Regional Conference Series in Mathematics) - Softcover

Richard F. Gundy

Softcover

ISBN 10: 0821807218 ISBN 13: 9780821807217

Publisher: American Mathematical Society, 1989

Synopsis

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 final topic centers on a discussion of the Ornstein-Uhlenbeck semigroup and P. A. Meyer's extension of the Riesz inequalities for the infinite-dimensional version of this semigroup. One of the major results of the book is the establishment of inequalities for the density of the area integral.

Edition details

• Publisher: American Mathematical Society
• Publication date: 1989
• Language: English
• ISBN 10: 0821807218
• ISBN 13: 9780821807217
• Binding: Paperback
• Number of pages: 49