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

Hiroshi Kawabi

Research output: Contribution to journalArticle

14 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 - Feb 2005
Externally publishedYes

Fingerprint

Harnack Inequality
Ginzburg-Landau
Transition Semigroup
Abbreviation
Stochastic Partial Differential Equations
Quantum Field Theory
Transition Probability
Estimate

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)
  • Analysis

Cite this

The parabolic Harnack inequality for the time dependent Ginzburg-Landau type SPDE and its application. / Kawabi, Hiroshi.

In: Potential Analysis, Vol. 22, No. 1, 02.2005, p. 61-84.

Research output: Contribution to journalArticle

@article{31d7ffe7326a4669a992f50af4e29843,
title = "The parabolic Harnack inequality for the time dependent Ginzburg-Landau type SPDE and its application",
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.",
keywords = "Gradient estimate, Parabolic Harnack inequality, SPDE, Varadhan type small time asymptotics",
author = "Hiroshi Kawabi",
year = "2005",
month = "2",
doi = "10.1007/s11118-003-6456-9",
language = "English",
volume = "22",
pages = "61--84",
journal = "Potential Analysis",
issn = "0926-2601",
publisher = "Springer Netherlands",
number = "1",

}

TY - JOUR

T1 - The parabolic Harnack inequality for the time dependent Ginzburg-Landau type SPDE and its application

AU - Kawabi, Hiroshi

PY - 2005/2

Y1 - 2005/2

N2 - 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.

AB - 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.

KW - Gradient estimate

KW - Parabolic Harnack inequality

KW - SPDE

KW - Varadhan type small time asymptotics

UR - http://www.scopus.com/inward/record.url?scp=15244361823&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=15244361823&partnerID=8YFLogxK

U2 - 10.1007/s11118-003-6456-9

DO - 10.1007/s11118-003-6456-9

M3 - Article

VL - 22

SP - 61

EP - 84

JO - Potential Analysis

JF - Potential Analysis

SN - 0926-2601

IS - 1

ER -