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2006.317: A study of stochastic differential equations with non-Lipschitzian coefficients

2006.317: Shizan Fang and Tusheng Zhang (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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DOI: 10.1007/s00440-004-0398-z

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 2000 > 34 Ordinary differential equations
MSC 2000 > 60 Probability theory and stochastic processes
MIMS number:2006.317
Deposited By:Miss Louise Stait
Deposited On:16 August 2006

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