Let M = {Mz, z∈R+2} be a continuous square integrable martingale and A = {Az, z∈R+2} be a continuous adapted increasing process. Consider the following stochastic partial differentialequations in the plane:dXz=α（z, Xz）dM2+β（z,Xz）dAz, z∈R+2,Xz=Zz, z∈R+2,where R+2=[0,+∞)×[0,+∞) and R+2 is its boundary, Z is a continuous stochastic process onR+2. We establish a new theorem on the pathwise uniqueness of solutions for the equation under aweaker condition than the Lipschitz one. The result concerning the one-parameter analogue of theproblem we consider here is immediate （see [1, Theorem 3.2]）. Unfortunately, the situation is muchmore complicated for two-parameter process and we believe that our result is the first one of its kindand is interesting in itself. We have proved the existence theorem for the equation in.
展开▼
机译：Finite Type System of Partial Differential Operators and Decomposition of Solutions of Partial Differential Equations (位相解析的方法による偏微分方程式论研究会及び散乱理论の数学研究会报告集)
