Sobolev differentiable flows of SDEs with local Sobolev and super-linear growth coefficients
Sobolev differentiable flows of SDEs with local Sobolev and super-linear growth coefficients
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DOI：
10.1214/15-aop1057
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发表时间：
2014-07
影响因子：
2.3
通讯作者：
Longjie Xie;Xicheng Zhang
中科院分区：
文献类型：
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作者：
Longjie Xie;Xicheng Zhang
通过建立随机场的Sobolev可微性的一个刻画，证明了具有局部Sobolev和超线性增长系数的随机微分方程解关于起始点的弱可微性.此外，我们还研究了伴随扩散半群的强Feller性质和不可约性。
By establishing a characterization for Sobolev differentiability of random fields, we prove the weak differentiability of solutions to stochastic differential equations with local Sobolev and super-linear growth coefficients with respect to the starting point. Moreover, we also study the strong Feller property and the irreducibility to the associated diffusion semigroup.