Portugaliae Mathematica   EMIS ELibM Electronic Journals PORTUGALIAE
MATHEMATICA
Vol. 61, No. 4, pp. 461-478 (2004)

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Euler scheme for solutions of stochastic differential equations with non-Lipschitz coefficients

A. Berkaoui

Department of Statistics, University of Warwick,
Gibbet Hill road, Coventry CV4 7AL -- UK
E-mail: berkaoui@stats.warwick.ac.uk

Abstract: Firstly, we investigate existence and uniqueness of solutions of stochastic differential equations when the coefficients are random Lipschitz or of class $C^1$. Secondly, we prove the strong convergence of the associated Euler scheme. The usual rates of convergence are obtained.

Keywords: stochastic differential equations; Euler scheme; strong approximation.

Classification (MSC2000): 60H10, 60H05, 60H35.

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Electronic version published on: 7 Mar 2008.

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