两参数Ito型随机微分方程解的收敛定理

The Convergence Theorem of the Solutions for Two-Parameter Ito Type Stochastic Differential Equations

设 wz 是 R2+ 上的布朗单 ,考虑两参数 Ito型随机微分方程 :dxz=a(z,xz) dwz +b(z,xz) dz (1)dxnz =an(z,xnz) dwz +bn(z,xnz) dz (2 )则在方程系数满足一定条件下 ,本文证明了方程 (2 )的解向方程 (1)

Let w z be Brown sheet on R 2 + . This paper is concerned with convergence theorem of the solutions for two parameter Ito type Stochastic Differential Equations of the form: d x z=a(z,x z) d w z+b(z,x z) d z(1) d x n z=a n(z,x n z) d w z+b n(z,x n z) d z(2) under suitable conditions on the functions involve in (1)(2).