关于含有未知过程局部时的随机微分方程的解

On the Solutions of Stochastic Differential Equations Involving the Local Times of the Unknown Processes

考虑了由 Brown运动驱动的含有未知过程局部时的一维随机微分方程 ,给出了其弱解存在和分布唯一的充分必要条件 ,并在此基础上对其强解进行了研究。将这些结果应用于一维时齐 Ito型方程 ,得到了在较弱条件下的相应结论。

Consider the stochastic differential equations involving the Brownian motion and the local times of unknown processes,and give the sufficient and necessary conditions for the existence and uniqueness in the sense of probability law of weak solutions.Based on the results on the weak solutions,we study the strong solutions.Applying these results to the time homogeneous It equations,we get the coresponding results under some weak conditions.