(1) I.M.B, UFR Sciences et techniques, Université de Bourgogne, 9 avenue Alain Savary, B.P. 47870, 21078 Dijon, France;(2) Department of Mathematics, University of Manchester, Oxford road, Manchester, M13 9PL, United Kingdom
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 Finally a large deviation principle of Freidlin-Wentzell type is also established in the paper.