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Euler scheme for SDEs with non-Lipschitz diffusion coefficient: strong convergence
Abdel Berkaoui, Mireille Bossy, Awa Diop
Journal:

ESAIM: Probability and Statistics / Volume 12 / 2008

Published online by Cambridge University Press:

13 November 2007, pp. 1-11

Print publication:

2008
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We consider one-dimensional stochastic differential equations in the particular case of diffusion coefficient functions of the form|x|α , α ∈ [1/2,1). In that case, we study the rate of convergence of asymmetrized version of the Euler scheme. This symmetrized version iseasy to simulate on a computer. We prove its strong convergence and obtain the same rate ofconvergence as when the coefficients are Lipschitz.

A symmetrized Euler scheme for an efficient approximation of reflected diffusions
Part of
- Probability theory and stochastic processes
- Parabolic equations and systems
Mireille Bossy, Emmanuel Gobet, Denis Talay
Journal:

Journal of Applied Probability / Volume 41 / Issue 3 / September 2004

Published online by Cambridge University Press:

14 July 2016, pp. 877-889

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September 2004
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In this article, we analyse the error induced by the Euler scheme combined with a symmetry procedure near the boundary for the simulation of diffusion processes with an oblique reflection on a smooth boundary. This procedure is easy to implement and, in addition, accurate: indeed, we prove that it yields a weak rate of convergence of order 1 with respect to the time-discretization step.

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2 results

Euler scheme for SDEs with non-Lipschitz diffusion coefficient: strong convergence

A symmetrized Euler scheme for an efficient approximation of reflected diffusions