Functional inequalities and an application for parabolic stochastic partial differential equations containing rotation
Functional inequalities and an application for parabolic stochastic partial differential equations containing rotation
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DOI：
10.1016/j.bulsci.2004.03.006
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发表时间：
2004-09
影响因子：
1.3
通讯作者：
Hiroshi Kawabi
中科院分区：
文献类型：
--
作者：
Hiroshi Kawabi
本文的主要目的是建立路径空间上关于吉布斯测度的非对称转移半群的梯度估计和抛物线哈纳克不等式。该半群与一个扩散过程有关，该扩散过程由某个包含旋转的抛物型随机偏微分方程（SPDE，缩写）的解来表示。我们还讨论了吉布斯测度和动态静态测度之间的关系。为了证明我们的函数不等式，我们为半群制定了一个合适的无穷小生成元域。作为我们结果的应用，我们研究了对动态转移概率的较低估计。
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.