The parabolic Harnack inequality for the time dependent Ginzburg-Landau type SPDE and its application

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15 Citations (Scopus)

Abstract

The main purpose of this paper is to establish the parabolic Harnack inequality for the transition semigroup associated with the time dependent Ginzburg-Landau type stochastic partial differential equation (=SPDE, in abbreviation). In view of quantum field theory, this dynamics is called a P(φ)1-time evolution. We prove the main result by adopting a stochastic approach which is different from Bakry-Emery's Γ2- method. As an application of our result, we study some estimates on the transition probability for our dynamics. We also discuss the Varadhan type asymptotics.

Original languageEnglish
Pages (from-to)61-84
Number of pages24
JournalPotential Analysis
Volume22
Issue number1
DOIs
Publication statusPublished - 2005 Feb
Externally publishedYes

Keywords

  • Gradient estimate
  • Parabolic Harnack inequality
  • SPDE
  • Varadhan type small time asymptotics

ASJC Scopus subject areas

  • Analysis

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