A bounded property for gradients of diffusion semigroups on Euclidean spaces

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Abstract

We consider uniformly elliptic diffusion processes X(t,x) on Euclidean spaces Rd, with some conditions in terms of the drift term (see assumptions A2 and A3). By using interpolation theory, we show a bounded property which gives an estimate of ∇xE[f(X(t,x))] involving |x| and ||f|| but not ||∇f||, and a power of 1/t smaller than 1.

Original languageEnglish
Pages (from-to)71-85
Number of pages15
JournalJournal of Functional Analysis
Volume216
Issue number1
DOIs
Publication statusPublished - 2004 Nov 1
Externally publishedYes

Keywords

  • Diffusion
  • Euclidean space
  • Gradient
  • Interpolation theory

ASJC Scopus subject areas

  • Analysis

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