The Parabolic Harnack Inequality for the Time Dependent Ginzburg–Landau Type SPDE and its Application
The Parabolic Harnack Inequality for the Time Dependent Ginzburg–Landau Type SPDE and its Application
复制标题
时变Ginzburg-Landau型SPDE抛物线Harnack不等式及其应用
DOI：
10.1007/s11118-003-6456-9
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发表时间：
2005
影响因子：
1.1
通讯作者：
Hiroshi Kawabi
中科院分区：
文献类型：
--
作者：
Hiroshi Kawabi
本文主要建立了含时Ginzburg-Landau型随机偏微分方程（=SPDE，简称SPDE）的转移半群的抛物Harnack不等式.根据量子场论，这种动力学称为aP（φ）1-时间演化。我们采用不同于Bakry-Emery的Γ2-方法的随机方法证明了主要结果。作为结果的应用，我们研究了动力学转移概率的一些估计。我们还讨论了Varadhan型渐近性。
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 aP(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.