Convergence of stochastic flows connected with stochastic ordinary differential equations
作者:
Kunita Hiroshi,
期刊:
Stochastics
(Taylor Available online 1986)
卷期:
Volume 17,
issue 3
页码: 215-251
ISSN:0090-9491
年代: 1986
DOI:10.1080/17442508608833391
出版商: Gordon and Breach Science Publishers, Inc
关键词: Stochastic flows;stochastic differential equations;approximation;weak convergence
数据来源: Taylor
摘要:
We obtain the limit theorem for the sequence of stochastic flows generated by the stochastic ordinary differential equations dx/dt = F$sub:n$esub:(t, x, ω)n =l, 2,.... Under some regularity and mixing conditions on the sequence F$sub:n$esub: n = l,2,..., it is shown that the associated flows converge weakly to a Brownian motion in the diffeomorphisms group and that the latter is generated by an Itô's stochastic differential equation. The strong convergence is also established: It covers the approximation theorems on stochastic flows studied by Malliavin. Ikeda Watanabe. Bismut and Shu.
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