Euler scheme for SDEs with non-Lipschitz diffusion coefficient: strong convergence
Abdel Berkaoui; Mireille Bossy; Awa Diop
ESAIM: Probability and Statistics (2007)
- 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 (2007): 1-11. <http://eudml.org/doc/104396>.
@article{Berkaoui2007,
abstract = {
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.
},
author = {Berkaoui, Abdel, Bossy, Mireille, Diop, Awa},
journal = {ESAIM: Probability and Statistics},
keywords = {Discretization scheme; strong convergence; CIR process.; discretization scheme; stochastic differential equations; Euler scheme},
language = {eng},
month = {11},
pages = {1-11},
publisher = {EDP Sciences},
title = {Euler scheme for SDEs with non-Lipschitz diffusion coefficient: strong convergence},
url = {http://eudml.org/doc/104396},
volume = {12},
year = {2007},
}
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
DA - 2007/11//
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|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.
LA - eng
KW - Discretization scheme; strong convergence; CIR process.; discretization scheme; stochastic differential equations; Euler scheme
UR - http://eudml.org/doc/104396
ER -
References
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- M. Bossy and A. Diop, Euler scheme for one dimensional SDEs with a diffusion coefficient function of the form |x|α, a in [ 1/2,1). Annals Appl. Prob. (Submitted).
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