A study of a class of stochastic differential equations with non-Lipschitzian coefficients

• 成果类型: Article
• 署名作者: Fang, SZ; Zhang, TS
• 署名单位: Universite Bourgogne Europe; University of Manchester
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-004-0398-z
• 发表日期: 2005
• 页码: 356-390
• 关键词: diffeomorphism group; diffusion-processes; large deviations; brownian-motion

摘要

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 1/vertical bar x-y vertical bar. Finally a large deviation principle of Freidlin-Wentzell type is also established in the paper.