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Riesz transform and integration by parts formulas for random variables

Authors
Journal
Stochastic Processes and their Applications
0304-4149
Publisher
Elsevier
Publication Date
Volume
121
Issue
6
Identifiers
DOI: 10.1016/j.spa.2011.02.006
Keywords
  • Riesz Transform
  • Integration By Parts
  • Malliavin Calculus
  • Sobolev Spaces

Abstract

Abstract We use integration by parts formulas to give estimates for the L p norm of the Riesz transform. This is motivated by the representation formula for conditional expectations of functionals on the Wiener space already given in Malliavin and Thalmaier (2006) [13]. As a consequence, we obtain regularity and estimates for the density of non-degenerated functionals on the Wiener space. We also give a semi-distance which characterizes the convergence to the boundary of the set of the strict positivity points for the density.

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