Journal article
Properties Of Solutions Of Stochastic Differential Equations With Nonhomogeneous Coefficients And Non-Lipschitz Diffusion
Year:
2009Published in:
Theory of Probability and Mathematical Statisticsstochastic differential equations
non-homogeneous coefficients
non-Lipschitz diffusion
limit theorem
L1 space
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.