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Abstract
We study one-dimensional stochastic differential equations with nonhomogeneous coefficients and non-Lipschitz diffusion. We prove some properties of the solutions of such equations and of the corresponding Euler scheme. We obtain the convergence rate of the Euler scheme for diffusions with weak singularity at zero.
Keywords.: Stochastic differential equation; nonhomogeneous coefficients; non-Lipschitz diffusion; Euler scheme; rate of convergence; local time
Received: 2009-06-01
Accepted: 2009-11-02
Published Online: 2011-02-10
Published in Print: 2011-March
© de Gruyter 2011
