文档介绍：?????D201077007 ????10487 ????????????????э????????????????????????????????????????????? ?????2014?5?17?万方数据 A Dissertation Submitted in Partial Ful?llment of the Requirements for the Degree of Doctor of Philosophy in Science Invariant Structures and Related Properties for Stochastic Dynamical Systems . Candidate : Zhongkai Guo Major : Probability Theory and Math- ematical Statistics Supervisor : Professor Jinqiao Duan Co-Supervisor : Huazhong University of Science &Technology Wuhan 430074, P. R. China May 2014 万方数据?????Ч????????????????????????????????????????????????????????Ч????????????????????????????Ч????????????????????????????Ч??????Ч????????Ч????????????? ??? ??????????????Ч???????????????????????????????????????????????????????????????Ф??????Ч????????????Ч????????????щ????????????????????????????????щЧ?????Ч??????¤????????Ч???????¤???????????√?? ????????? ??? ?????????? ??? ???万方数据???????????????????????.???????????????????????????????????????????.????????????????М???????????????????????????,????????????????????. Ч??????????????????э???????,????????. ?????,??????????,??????,????????????Ч??. ?????,???????????ш????????????э??????,?????????э???????Я?. ??,????????? ??????????u ?t ? Pnk,j=1 ? x k(a kj(x)? x ju) +a 0(x)u=f(u) +2 ˙W 1on D , ?u ?t + Pnk,j=1 ν ka kj(x)? x ju+c(x)u=g(u) +2 ˙W 2 on ?D, u(0, x) =u 0(x) on D×?D, ?? D?R n,?? W 1, W 2????????(?,F,F t,P)??????????Wiener??.????ш??????? t?????????,????????????ш???.??????????????????э??????,???2→0????????????????????ш?????э???????ш????э???????Я???. ?????,??????????????????????????Я?,?????????dudt =Au+F(u) +σu±˙w, ?? w???????,?? A???????????????????.?????? F,??????? C k???.??±??????Stratanovich????????.???????????????????????,???????(Stochastic)?????????э????????(Random)?? I 万方数据??.???????????,??????????Random??????Lyapunov-Perron???????Я?,??????????э???????????????????????Я???. ?????,???????????????????,??????? ????????? du+Audt=f(u)dt+g(u)dw(t), in D×(0, T], u= 0, on ?D×(0, T], u(0) =u 0, in D, ????????