随机偏微分方程解的稳定性  

ON THE STABILITY OF THE SOLUTION FOR THE STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS

作　　者：罗少波[1] 

机构地区：[1]中国科学院应用数学研究所

出　　处：《应用概率统计》1989年第2期127-137,共11页Chinese Journal of Applied Probability and Statistics

摘　　要：本文讨论了随机偏微分方程当其一、二阶微分算子之系数及初始条件扰动时,其解的稳定性。同时,也讨论了在非线性滤波理论中导出的测度值随机偏微分方程,即所谓Zakai方程,当其一、二阶微分算子之系数及初始条件扰动时,其解的稳定性。The stability of the solution for the stochastic partial differential equation is considered in this paper, when the initial condition and the coefficients of the first and seeond order differential operators are subject to small perturbations. Also discussed is the stability of the Zakai equation which is a stochastic partial differential equation for measure valued process ari sing in non-linear filtering theory. The powerful tools are the theory of backward stochastic Stratonovioh differontial equations and Ito's baokward formula.

关 键 词：随机偏微分方程 解 稳定性 Zakai方程 

分 类 号：O211.63[理学—概率论与数理统计]