Stochastic differential equations with non-Lipschitz coeffic

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tochastic differential equations with non-Lipschitz coefficients
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arXiv:math.PR/0311032 v1 4 Nov 2003
Stochastic differential equations with
non-Lipschitz coefficients: I. Pathwise
uniqueness and Large deviations
Shizan FANG and Tusheng ZHANG
I.M.B, UFR Sciences et techniques, Universit´e de Bourgogne, 9 avenue Alain
Savary, B.P. 47870, 21078 Dijon, France.
Department of Mathematics, University of Manchester, Oxford road, Manch-
ester, M13 9PL, England.
Abstract
We study a class of stochastic differential equations with non-Lipschitzian
coefficients. A unique strong solution is obtained and a large deviation
principle of Freidlin-Wentzell type has been established.