# 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

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topBerkaoui, 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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