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

Abdel Berkaoui; Mireille Bossy; Awa Diop

ESAIM: Probability and Statistics (2008)

  • Volume: 12, page 1-11
  • ISSN: 1292-8100

Abstract

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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 a symmetrized version of the Euler scheme. This symmetrized version is easy to simulate on a computer. We prove its strong convergence and obtain the same rate of convergence as when the coefficients are Lipschitz.

How to cite

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Berkaoui, Abdel, Bossy, Mireille, and Diop, Awa. "Euler scheme for SDEs with non-Lipschitz diffusion coefficient : strong convergence." ESAIM: Probability and Statistics 12 (2008): 1-11. <http://eudml.org/doc/246056>.

@article{Berkaoui2008,
abstract = {We consider one-dimensional stochastic differential equations in the particular case of diffusion coefficient functions of the form $|x|^\alpha $, $\alpha \in [1/2,1)$. In that case, we study the rate of convergence of a symmetrized version of the Euler scheme. This symmetrized version is easy to simulate on a computer. We prove its strong convergence and obtain the same rate of convergence as when the coefficients are Lipschitz.},
author = {Berkaoui, Abdel, Bossy, Mireille, Diop, Awa},
journal = {ESAIM: Probability and Statistics},
keywords = {discretization scheme; strong convergence; CIR process; stochastic differential equations; Euler scheme},
language = {eng},
pages = {1-11},
publisher = {EDP-Sciences},
title = {Euler scheme for SDEs with non-Lipschitz diffusion coefficient : strong convergence},
url = {http://eudml.org/doc/246056},
volume = {12},
year = {2008},
}

TY - JOUR
AU - Berkaoui, Abdel
AU - Bossy, Mireille
AU - Diop, Awa
TI - Euler scheme for SDEs with non-Lipschitz diffusion coefficient : strong convergence
JO - ESAIM: Probability and Statistics
PY - 2008
PB - EDP-Sciences
VL - 12
SP - 1
EP - 11
AB - We consider one-dimensional stochastic differential equations in the particular case of diffusion coefficient functions of the form $|x|^\alpha $, $\alpha \in [1/2,1)$. In that case, we study the rate of convergence of a symmetrized version of the Euler scheme. This symmetrized version is easy to simulate on a computer. We prove its strong convergence and obtain the same rate of convergence as when the coefficients are Lipschitz.
LA - eng
KW - discretization scheme; strong convergence; CIR process; stochastic differential equations; Euler scheme
UR - http://eudml.org/doc/246056
ER -

References

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  3. [3] M. Bossy and A. Diop, Euler scheme for one dimensional SDEs with a diffusion coefficient function of the form | x | a , a in [1/2,1). Annals Appl. Prob. (Submitted). 
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