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2014 Strong completeness for a class of stochastic differential equations with irregular coefficients
Xin Chen, Xue-Mei Li
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Electron. J. Probab. 19: 1-34 (2014). DOI: 10.1214/EJP.v19-3293

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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Xin Chen. Xue-Mei Li. "Strong completeness for a class of stochastic differential equations with irregular coefficients." Electron. J. Probab. 19 1 - 34, 2014. https://doi.org/10.1214/EJP.v19-3293

Information

Accepted: 3 October 2014; Published: 2014
First available in Project Euclid: 4 June 2016

zbMATH: 1307.60074
MathSciNet: MR3272324
Digital Object Identifier: 10.1214/EJP.v19-3293

Subjects:
Primary: 60H10

Keywords: approximation , derivative flow equation , differential formula , Stochastic differential equation , strong completeness

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