Strong completeness for a class of stochastic differential equations with irregular coefficients

Xin Chen (Universidade de Lisboa)
Xue-Mei Li (The University of Warwick)

Abstract


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.

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Pages: 1-34

Publication Date: October 3, 2014

DOI: 10.1214/EJP.v19-3293

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