论文标题
具有非平滑系数的ITô-Stochastic微分方程的分析理论
Analytic theory of Itô-stochastic differential equations with non-smooth coefficients
论文作者
论文摘要
我们提供了对系数局部规则性假设较低的非分类时间均匀的ITô-Systocative微分方程的详细分析。特别是漂移系数只能满足局部可集成性条件。我们讨论了非探索，不可减至性，Krylov类型估计值，过渡功能和解决方案的规律性，瞬间不平等，复发性，瞬时，过渡函数的长时间行为，不变性度量的存在和独特性，以及路径独特性，强大的解决方案，强大的解决方案和在法律中的独特性。该分析特别表明，可以得出各种上述特性的清晰明确条件，类似于具有局部Lipschitz系数的经典随机微分方程。
We present a detailed analysis of non-degenerate time-homogeneous Itô-stochastic differential equations with low local regularity assumptions on the coefficients. In particular the drift coefficient may only satisfy a local integrability condition. We discuss non-explosion, irreducibility, Krylov type estimates, regularity of the transition function and resolvent, moment inequalities, recurrence, transience, long time behavior of the transition function, existence and uniqueness of invariant measures, as well as pathwise uniqueness, strong solutions and uniqueness in law. This analysis shows in particular that sharp explicit conditions for the various mentioned properties can be derived similarly to the case of classical stochastic differential equations with local Lipschitz coefficients.
