A study of stochastic differential equations with non-Lipschitzian coefficients

Fang, Shizan and Zhang, Tusheng (2003) A study of stochastic differential equations with non-Lipschitzian coefficients. Probability Theory and Related Fields, 132 (3). pp. 356-390. ISSN 1432-2064

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Abstract

We study a class of stochastic differential equations with non-Lipschitz coefficients. A unique strong solution is obtained and the non confluence of the solutions of stochastic differential equations is proved. The dependence with respect to the initial values is investigated. To obtain a continuous version of solutions, the modulus of continuity of coefficients is assumed to be less than |x-y| log MediaObjects/s00440-004-0398-zflb1.gif Finally a large deviation principle of Freidlin-Wentzell type is also established in the paper.

Item Type: Article
Uncontrolled Keywords: Gronwall lemma - Non-Lipschitz conditions - Pathwise uniqueness - Non-explosion - Non confluence - Large deviation principle - Euler approximation
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 34 Ordinary differential equations
MSC 2010, the AMS's Mathematics Subject Classification > 60 Probability theory and stochastic processes
Depositing User: Ms Lucy van Russelt
Date Deposited: 16 Aug 2006
Last Modified: 20 Oct 2017 14:12
URI: http://eprints.maths.manchester.ac.uk/id/eprint/526

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