论文标题
局部生长奇异漂移的随机微分方程
Stochastic Differential Equations with Local Growth Singular Drifts
论文作者
论文摘要
在本文中，我们研究了全球强大差分方程，相关扩散半群的强大特性以及全球随机流属性的弱点，其中奇异漂移$ b $和sobolev diffusion $σ$的弱梯度应该满足Sobolev diffusion $σ$的弱梯度，以满足$ | | | | | ______________ | o（（（\ log r）^{{（（p_1-d）^2}/{2p^2_1}}）$和$ || \ nablaσ（x）1_ {| x | x | \ le r} || _ {p_1} （{r}/{3}））^{（p_1-d）^2}/{2p^2_1}}）$。这些结果的主要工具是全局两点运动的分解，Krylov的估计值，Khasminskii的估计值，Zvonkin的转换以及随机场的Sobolev不同性能的表征。
In this paper, we study the weak differentiability of global strong solution of stochastic differential equations, the strong Feller property of the associated diffusion semigroups and the global stochastic flow property in which the singular drift $b$ and the weak gradient of Sobolev diffusion $σ$ are supposed to satisfy $||b(x){1}_{|x|\le R}||_{p_1}\le O((\log R)^{{(p_1-d)^2}/{2p^2_1}})$ and $||\nabla σ(x)1_{|x|\le R} ||_{p_1} \le O((\log ({R}/{3}))^{{(p_1-d)^2}/{2p^2_1}})$ respectively. The main tools for these results are the decomposition of global two-point motions, Krylov's estimate, Khasminskii's estimate, Zvonkin's transformation and the characterization for Sobolev differentiability of random fields.
