Stochastic differential equtions with non-lipschitz coefficients:II. Dependence with respect to initial values

Details Stochastic differential equtions with non-lipschitz coefficients:II. Dependence with respect to initial values Stochastic differential equtions with non-lipschitz coefficients:II. Dependence with respect to initial values

2003-11-04

arxiv.org/abs/math/0311034v1

Mathematics

Probability

14 pages

Scientific paper

The existence of the unique strong solution for a class of stochastic differential equations with non-Lipschitz coefficients was established recently. In this paper, we shall investigate the dependence with respect to the initial values. We shall prove that the non confluence of solutions holds under our general conditions. To obtain a continuous version, the modulus of continuity of coefficients is assumed to be less than $\dis |x-y|\log{1\over|x-y|}$. In this case, it will give rise to a flow of homeomorphisms if the coefficients are compactly supported.

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