Strong solutions of SDES with singular drift and Sobolev diffusion coefficients

In this paper we prove the existence of a unique strong solution up to the explosion time for an SDE with a uniformly non-degenerate Sobolev diffusion coefficient (non-Lipschtiz) and locally integrable drift coefficient. Moreover, two non-explosion conditions are given.

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Bibliographic Details
Published in:Stochastic processes and their applications 2005-11, Vol.115 (11), p.1805-1818
Main Author: Zhang, Xicheng
Format: Article
Language:English
Subjects:
Exact sciences and technology
Krylov's estimate
Mathematics
Probability and statistics
Probability theory and stochastic processes
Sciences and techniques of general use
Sobolev space
Stochastic analysis
Stochastic processes
Strong solution
Strong solution Krylov's estimate Zvonkin's transformation Sobolev space
Zvonkin's transformation
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Description
Summary:In this paper we prove the existence of a unique strong solution up to the explosion time for an SDE with a uniformly non-degenerate Sobolev diffusion coefficient (non-Lipschtiz) and locally integrable drift coefficient. Moreover, two non-explosion conditions are given.
ISSN:0304-4149
1879-209X
DOI:10.1016/j.spa.2005.06.003