An estimate of the rate of convergence of an approximating scheme applied to a stochastic differential equation with an additional parameter

Authors:
Yu. S. Mishura and A. V. Shvaĭ

Translated by:
S. Kvasko

Original publication:
Teoriya Imovirnostei ta Matematichna Statistika, tom **82** (2010).

Journal:
Theor. Probability and Math. Statist. **82** (2011), 75-85

MSC (2010):
Primary 60H10

DOI:
https://doi.org/10.1090/S0094-9000-2011-00828-9

Published electronically:
August 4, 2011

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We consider a stochastic differential equation with a diffusion coefficient involving an additional process viewed as a parameter. Given a rate of convergence of the Euler approximations for this parameter, we find the mean square rate of convergence of the Euler approximation scheme. An example is considered where the parameter is driven by a fractional Brownian motion.

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Additional Information

**Yu. S. Mishura**

Affiliation:
Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue 2, Kiev 03127, Ukraine

Email:
myus@univ.kiev.ua

**A. V. Shvaĭ**

Affiliation:
Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue 2, Kiev 03127, Ukraine

Email:
ShvajSS@ukr.net

DOI:
https://doi.org/10.1090/S0094-9000-2011-00828-9

Keywords:
Fractional Brownian motion,
approximate solution of stochastic differential equations

Received by editor(s):
July 8, 2009

Published electronically:
August 4, 2011

Additional Notes:
The first author is indebted to the European Commission for support in the framework of the “Marie Curie Actions” program, grant PIRSES-GA-2008-230804

The second author, Alexander Shvaĭ, died tragically on October 10, 2010, after the original Ukrainian issue had already been published

Article copyright:
© Copyright 2011
American Mathematical Society