Functional inequalities and an application for parabolic stochastic partial differential equations containing rotation

Hiroshi Kawabi

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

The main purpose of this paper is to establish a gradient estimate and a parabolic Harnack inequality for the non-symmetric transition semigroup with respect to the Gibbs measure on a path space. This semigroup is related to a diffusion process which is represented by the solution of a certain parabolic stochastic partial differential equation (SPDE, in abbreviation) containing rotation. We also discuss the relationship between the Gibbs measure and stationary measures of our dynamics. For the proof of our functional inequalities, we formulate a suitable domain of the infinitesimal generator for the semigroup. As an application of our results, we study a certain lower estimate on the transition probability for our dynamics.

Original languageEnglish
Pages (from-to)687-725
Number of pages39
JournalBulletin des Sciences Mathematiques
Volume128
Issue number8
DOIs
Publication statusPublished - Sep 2004
Externally publishedYes

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Keywords

  • Gibbs measure
  • Gradient estimate
  • Parabolic Harnack inequality
  • Rotation
  • SPDE
  • Transition probability

ASJC Scopus subject areas

  • Mathematics(all)

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