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Publication Date:
December 2011
ISSN:
1569-397X
DOI:
10.1515/ROSE.2011.021

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Editor-in-Chief: Girko, Vyacheslav

Managing Editor: Molchanov, S.

null Accardi, L. / Albeverio, Sergio / Carmona, R. / Casati, G. / Christopeit, N. / Domanski, C. / Drygas, Hilmar / Evstigneev, Igor / Gupta, A.K. / Ibragimov, I. / Kirsch, Werner / Klein, A. / Kondratyev, Yuri / Kurotschka, V. / Leonenko, N. / Loubaton, Philippe / Orsingher, E. / Pastur, L. / Rodrigues, Waldyr A. / Shiryaev, Albert / Turbin, A.F.

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Rate of convergence of Euler approximations of solution to mixed stochastic differential equation involving Brownian motion and fractional Brownian motion

1Department of Probability, Statistics and Actuarial Mathematics, Mechanics and Mathematics Faculty, Kyiv Taras Shevchenko National University, Volodymyrska, 60, 01601 Kyiv, Ukraine.

Citation Information: Random Operators and Stochastic Equations. Volume 19, Issue 4, Pages 387–406, ISSN (Online) 1569-397x, ISSN (Print) 0926-6364, DOI: 10.1515/ROSE.2011.021, December 2011

Publication History:

Received: 28/09/2010;
Accepted: 12/02/2011;
Published Online: 01/03/2012

Abstract

We consider a mixed stochastic differential equation involving both standard Brownian motion and fractional Brownian motion with Hurst parameter H > 1/2. The mean-square rate of convergence of Euler approximations of solution to this equation is obtained.

Keywords.: Fractional Brownian motion; mixed stochastic differential equation; pathwise integral; Euler approximation

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