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

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 continuou...

Full description

Saved in:
Bibliographic Details
Published in:Probability theory and related fields 2005-07, Vol.132 (3), p.356-390
Main Authors: Fang, Shizan, Zhang, Tusheng
Format: Article
Language:English
Subjects:
Coefficients
Differential equations
Eulers equations
Exact sciences and technology
Explosions
Hypotheses
Markov processes
Mathematical analysis
Mathematics
Ordinary differential equations
Probability
Probability and statistics
Probability theory and stochastic processes
Sciences and techniques of general use
Stochastic analysis
Stochastic models
Studies
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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/|x-y|. Finally a large deviation principle of Freidlin-Wentzell type is also established in the paper. [PUBLICATION ABSTRACT]
ISSN:0178-8051
1432-2064
DOI:10.1007/s00440-004-0398-z