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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