两指标随机积分方程解的唯一性

UNIQUENESS OF SOLUTION FOR TWO——PARAMETER STOCHASTIC INTEGRAL EQUATIONS

在正交增量鞅的随机积分基础上，利用Ｌｉｐｓｃｈｉｔｚ条件，讨论了下面一类两参数随机积分方程解的唯一性．Ｘ（ｓ，ｔ）＝Ｚ（ｓ，０）＋Ｚ（０，ｔ）－Ｚ（０，０）＋∫Ｒｓｔα（ｕ，ｖ，Ｘ）ｄＭｕｖ＋∫Ｒｓｔβ（ｕ，ｖ，Ｘ）ｄｍｕｖ＋∫Ｒ２ｓｔγ１（ｕ，ｖ，ｕ′，ｖ′，Ｘ）ｄＭｕｖｄＭｕ′ｖ′＋∫Ｒ２ｓｔγ２（ｕ，ｖ，ｕ′，ｖ′，Ｘ）ｄＭｕｖｄｍｕ′ｖ′＋∫Ｒ２ｓｔγ３（ｕ，ｖ，ｕ′，ｖ′，Ｘ）ｄｍｕｖｄＭｕ′ｖ′．其中α、β、γｉ，ｉ＝１，２，３均属于相应的泛函空间，｛ＭＺ｝是满足［Ｍ］Ｚ＝ＣＺ的Ｒ２＋上正交增量鞅，ｍ是Ｒ２＋上的Ｌｅｂｅｓｑｕｅ测度．

The unique of following two——parameter stochastic integral equations is proved with the lipschitz conditions X(s,t)=Z(s,0)+Z(0,t)-Z(0,0)+∫ R st α(u,v,X)dM uv +∫ R st β(u,v,X)dM uv +∫ R 2 st r 1(u,v,u′,v′,X)dM uv dM u′v′ +∫ R 2 st r 2(u,v,u′,v′,X)dM uv dm u′v′ +∫ R 2 st r 3(u,v,u′,v′,X)dm uv dM u′v′ . here α、β、r i,i=1,2,3 belong to individual functional spaces, {M Z} is a martingale with orthogonal increments on R 2 +. m is the measure with Lebesque on R 2 +.