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

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 1/x y. Finally a large deviation principle of Freidlin-Wentzell type is also established in the paper. © Springer-Verlag 2005.