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Some Topics in Probability and Analysis
 
A co-publication of the AMS and CBMS
Some Topics in Probability and Analysis
Softcover ISBN:  978-0-8218-0721-7
Product Code:  CBMS/70
List Price: $28.00
Individual Price: $22.40
eBook ISBN:  978-1-4704-2430-5
Product Code:  CBMS/70.E
List Price: $26.00
Individual Price: $20.80
Softcover ISBN:  978-0-8218-0721-7
eBook: ISBN:  978-1-4704-2430-5
Product Code:  CBMS/70.B
List Price: $54.00 $41.00
Some Topics in Probability and Analysis
Click above image for expanded view
Some Topics in Probability and Analysis
A co-publication of the AMS and CBMS
Softcover ISBN:  978-0-8218-0721-7
Product Code:  CBMS/70
List Price: $28.00
Individual Price: $22.40
eBook ISBN:  978-1-4704-2430-5
Product Code:  CBMS/70.E
List Price: $26.00
Individual Price: $20.80
Softcover ISBN:  978-0-8218-0721-7
eBook ISBN:  978-1-4704-2430-5
Product Code:  CBMS/70.B
List Price: $54.00 $41.00
  • Book Details
     
     
    CBMS Regional Conference Series in Mathematics
    Volume: 701989; 49 pp
    MSC: Primary 60;

    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.

    Readership

  • Table of Contents
     
     
    • Chapters
    • Introduction
    • The Barlow-Yor Inequalities
    • The Density of the Area Integral
    • Norm Inequalities for $D$
    • Local Estimates
    • Terminal Expectations and Singular Integrals
    • The Ornstein-Uhlenbeck Semigroup
    • P. A. Meyer’s Riesz Transform Inequalities
    • The Ornstein-Uhlenbeck Process for the Rademacher Functions
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 701989; 49 pp
MSC: Primary 60;

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.

Readership

  • Chapters
  • Introduction
  • The Barlow-Yor Inequalities
  • The Density of the Area Integral
  • Norm Inequalities for $D$
  • Local Estimates
  • Terminal Expectations and Singular Integrals
  • The Ornstein-Uhlenbeck Semigroup
  • P. A. Meyer’s Riesz Transform Inequalities
  • The Ornstein-Uhlenbeck Process for the Rademacher Functions
Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.