The rate of convergence of the Euler scheme to the solution of stochastic differential equations with nonhomogeneous coefficients and non-Lipschitz diffusion

Yuliya S. Mishura; Svitlana V. Posashkova

doi:10.1515/ROSE.2011.003

Published by De Gruyter February 10, 2011

The rate of convergence of the Euler scheme to the solution of stochastic differential equations with nonhomogeneous coefficients and non-Lipschitz diffusion

Yuliya S. Mishura

and Svitlana V. Posashkova

From the journal

https://doi.org/10.1515/ROSE.2011.003

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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

The rate of convergence of the Euler scheme to the solution of stochastic differential equations with nonhomogeneous coefficients and non-Lipschitz diffusion

Abstract

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