两指标随机微分方程的弱解和分布唯一性

WEAK SOLUTION TO TWO-PARAMETER STOCHASTIC DIFFERENTIAL EQUATION AND PROBABILITY DISTRIBUTION UNIQUENESS

本文定义了两指标随机微分方程(?)解的轨道唯一性和分布唯一性,进而研究了轨道唯一性和分布唯一性之间的关系,得出了两指标 Watanabe-Yamada 定理,并且得到了随机边界条件下方程(1)强解存在的充要条件。

The definitions of pathwise uniqueness and probability distribution of so-lution to two parameter stochastic differential equations(?)(1)has been given.Moreover,the relationship between pathwise uniqueness andprobability distribution uniqueness has been considered.The two-parameterWatanabe-Yamada theorem,the necessary and sufficent condition of existenceof strong solution to equation(1)with stochastic boundary is abtained.