Strong completeness for a class of stochastic differential equations with irregular coefficients
Strong completeness for a class of stochastic differential equations with irregular coefficients
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DOI：
10.1214/ejp.v19-3293
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发表时间：
2014-02
影响因子：
1.4
通讯作者：
Xin Chen;Xue-Mei Li
中科院分区：
文献类型：
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作者：
Xin Chen;Xue-Mei Li
我们证明了一类非退化SDEs的强完备性，这类SDEs的系数不一定是一致椭圆的，也不一定是局部Lipschitz连续的或有界的。此外，对于每一个$p>0$，存在一个正数$T(p)$，使得对于所有$T <T(p)$，解流$F_t(\cdot)$属于Sobolev空间$W_{loc}^{1,p}$。这方面的主要工具是对相关的导数流动方程的近似。作为应用，还得到了一个微分公式。
We prove the strong completeness for a class of non-degenerate SDEs, whose coefficients are not necessarily uniformly elliptic nor locally Lipschitz continuous nor bounded.Moreover, for each $p>0$ there is a positive number $T(p)$ such that for all $t<T(p)$,the solution flow $F_t(\cdot)$ belongs to the Sobolev space $W_{loc}^{1,p}$. The main tool for this is the approximation of the associated derivative flow equations. As an application a differential formula is also obtained.