Gradient estimates and applications for SDEs in Hilbert space with multiplicative noise and Dini continuous drift

被引：29
|
作者：
Wang, Feng-Yu [1 ,2 ]
机构：
[1] Beijing Normal Univ, Sch Math Sci, Beijing 100875, Peoples R China
[2] Swansea Univ, Dept Math, Singleton Pk, Swansea SA2 8PP, W Glam, Wales
来源：
JOURNAL OF DIFFERENTIAL EQUATIONS | 2016年 / 260卷 / 03期
关键词：
Semi-linear SPDE; Mild solution; Log-Holder drift; Multiplicative noise; Strong Feller property; STOCHASTIC-EVOLUTION EQUATIONS; LOG-HARNACK INEQUALITY; DIFFERENTIAL-EQUATIONS; STRONG UNIQUENESS; MEASURABLE DRIFT; TERM;
D O I：
10.1016/j.jde.2015.10.020
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Consider the stochastic evolution equation in a separable Hilbert space FA with a nice multiplicative noise and a locally Dini continuous drift. We prove that for any initial data the equation has a unique (possibly explosive) mild solution. Under a reasonable condition ensuring the non-explosion of the solution, the strong Feller property of the associated Markov semigroup is proved. Gradient estimates and log-Harnack inequalities are derived for the associated semigroup under certain global conditions, which are new even in finite-dimensions. (C) 2015 Elsevier Inc. All rights reserved.
引用
收藏
页码：2792 / 2829
页数：38
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