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Theory of Probability and Mathematical Statistics
Theory of Probability and Mathematical Statistics
ISSN 1547-7363(online) ISSN 0094-9000(print)

 

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
Published electronically: August 4, 2011
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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: http://dx.doi.org/10.1090/S0094-9000-2011-00828-9
PII: S 0094-9000(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