On the decomposition of solutions of stochastic differential equations
On the decomposition of solutions of stochastic differential equations
复制标题
随机微分方程解的分解
DOI：
10.1007/bfb0088729
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发表时间：
1981
影响因子：
1.1
通讯作者：
H. Kunita
中科院分区：
文献类型：
--
作者：
H. Kunita
L j=L，其中Xl“，Xr是流形M上的光滑向量场，···是连续的半鞅。符号0表示Stratonovich积分。在本文的第一部分(第1-3节)中，我们将证明在XL‘···Xr或M上的附加条件下，当这一性质在最近的随机微分几何研究中显得重要时，映射成为微分同胚流，并且已经被几位作者研究过，如Elworth[7]，Malliavin US]，Ikeda-Watanabe[8]。铋[1]。这里我们将提出另一种证明微分同胚的方法。在第一节中，我们考虑的是Ito BDE，而不是Stratonovich SDE。我们将证明，如果系数是Lipschitz，则Ito SDE的解映射是同胚流
L j= l where Xl"", X r are smooth vector fields on a manifold M, and•••• are continuous semimartingales. The symbol 0 denotes the Stratonovich integral. We denote the solution with initial condition= x as or Then defines a map from M into itself for each t and asw In the first part of the paper (Sections 1-3), we will show that under additional contitions on Xl'•••• X r or M. the maps become a flow of diffeomorphisms asw The property appears important in recent study of stochastic differential geometry, and has been studied by several authors, eg Elworthy [7], Malliavin US], Ikeda-Watanabe [8]. Bismut [1]. We will propose here still other method for the proof of diffeomorphism. In Section 1 we consider Ito BDE's rather than Stratonovich SDE's on We will prove that the solution map of Ito SDE is a flow of homeomorphisms, provided that coefficients are Lipschitz