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

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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.

元の言語English
ページ(範囲)687-725
ページ数39
ジャーナルBulletin des Sciences Mathematiques
128
発行部数8
DOI
出版物ステータスPublished - 2004 9 1
外部発表Yes

ASJC Scopus subject areas

  • Mathematics(all)

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