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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