Properties Of Solutions Of Stochastic Differential Equations With Nonhomogeneous Coefficients And Non-Lipschitz Diffusion

Properties of solutions of stochastic differential equations with nonhomo- geneous coefficients and non-Lipschitz diffusion are studied in the paper. Conditions on the coefficients of an equation are obtained ensuring that a solution does not vanish over a finite time interval in the case of the diffusion (formula presented). We prove a limit theorem that solutions continuously depend on the parameter n in the space L1(P) for a sequence of stochastic differential equations with nonhomogeneous coefficients and non-Lipschitz diffusion.