Properties of solutions of stochastic differential equations with nonhomogeneous coefficients and non-Lipschitz diffusion
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Properties of solutions of stochastic differential equations with nonhomogeneous 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 $\sigma (t)\sqrt {x}$. We prove a limit theorem that solutions continuously depend on the parameter $n$ in the space $L_1(\mathsf {P})$ for a sequence of stochastic differential equations with nonhomogeneous coefficients and non-Lipschitz diffusion.
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