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Random Operators and Stochastic Equations

Editor-in-Chief: Girko, Vyacheslav

Managing Editor: Molchanov, S.

Editorial Board Member: Accardi, L. / Albeverio, Sergio / Carmona, R. / Casati, G. / Christopeit, N. / Domanski, C. / Drygas, Hilmar / 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. / Veretennikov, Alexandre

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CiteScore 2016: 0.37

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Source Normalized Impact per Paper (SNIP) 2016: 0.793

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1569-397X
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Volume 19, Issue 4 (Jan 2011)

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

Yuliya S. Mishura
  • Department of Probability, Statistics and Actuarial Mathematics, Mechanics and Mathematics Faculty, Kyiv Taras Shevchenko National University, Volodymyrska, 60, 01601 Kyiv, Ukraine.
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/ Georgiy M. Shevchenko
  • Department of Probability, Statistics and Actuarial Mathematics, Mechanics and Mathematics Faculty, Kyiv Taras Shevchenko National University, Volodymyrska, 60, 01601 Kyiv, Ukraine.
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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

About the article

Received: 2010-09-28

Accepted: 2011-02-12

Published in Print: 2011-12-01


Citation Information: Random Operators and Stochastic Equations, ISSN (Online) 1569-397x, ISSN (Print) 0926-6364, DOI: https://doi.org/10.1515/ROSE.2011.021.

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