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The rate of convergence of the Euler scheme to the solution of stochastic differential equations with nonhomogeneous coefficients and non-Lipschitz diffusion
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Yuliya S. Mishura
and
Svitlana V. Posashkova
Published/Copyright:
February 10, 2011
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
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- Use of the global implicit function theorem to induce singular conditional distributions on surfaces in n dimensions: Part II
- BSDEs driven by infinite dimensional martingales and their applications to stochastic optimal control
- The rate of convergence of the Euler scheme to the solution of stochastic differential equations with nonhomogeneous coefficients and non-Lipschitz diffusion
- A characterization of the geometric Brownian motion in terms of infinite dimensional Laplacians
Keywords for this article
Stochastic differential equation;
nonhomogeneous coefficients;
non-Lipschitz diffusion;
Euler scheme;
rate of convergence;
local time
Articles in the same Issue
- Use of the global implicit function theorem to induce singular conditional distributions on surfaces in n dimensions: Part II
- BSDEs driven by infinite dimensional martingales and their applications to stochastic optimal control
- The rate of convergence of the Euler scheme to the solution of stochastic differential equations with nonhomogeneous coefficients and non-Lipschitz diffusion
- A characterization of the geometric Brownian motion in terms of infinite dimensional Laplacians
