Harnack Inequalities for SDEs with Multiplicative Noise and Non-regular Drift
Harnack Inequalities for SDEs with Multiplicative Noise and Non-regular Drift
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DOI：
10.1142/s021949371550015x
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发表时间：
2013-10
期刊：
影响因子：
--
通讯作者：
Huaiqian Li;Dejun Luo;Jian Wang
中科院分区：
文献类型：
--
作者：
Huaiqian Li;Dejun Luo;Jian Wang
在引用文献[Flandoli，Zhang 11]的基础上，建立了具有非退化扩散系数和非正则时变漂移系数的随机微分方程半群的Log-Harnack不等式和幂Harnack不等式.我们考虑了两种情况：(1)漂移满足LPS型可积性，(2)漂移关于空间变量是一致H_(？)连续的.最后，利用带漂移的稳定过程的显式热核估计，证明了对称稳定过程驱动的随机微分方程的Harnack不等式.
The log-Harnack inequality and Harnack inequality with powers for semigroups associated to SDEs with non-degenerate diffusion coefficient and non-regular time-dependent drift coefficient are established, based on the recent papers \cite{Flandoli, Zhang11}. We consider two cases in this work: (1) the drift fulfills the LPS-type integrability, and (2) the drift is uniformly H\"older continuous with respect to the spatial variable. Finally, by using explicit heat kernel estimates for the stable process with drift, the Harnack inequality for the stochastic differential equation driven by symmetric stable process is also proved.