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

 

Continuous dependence of solutions of stochastic differential equations driven by standard and fractional Brownian motion on a parameter


Authors: Yu. S. Mishura, S. V. Posashkova and S. V. Posashkov
Translated by: S. Kvasko
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 83 (2010).
Journal: Theor. Probability and Math. Statist. 83 (2011), 111-126
MSC (2010): Primary 60G22; Secondary 60H10
Published electronically: February 2, 2012
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Abstract | References | Similar Articles | Additional Information

Abstract: We consider a stochastic differential equation driven by both a Wiener process and a fractional Brownian motion. The coefficients of the equation are nonhomogeneous, and the initial condition is random. It is assumed that both the coefficients and the initial condition depend on a parameter. We establish conditions on the coefficients and the initial condition for the continuous dependence of a solution on the parameter.


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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

S. V. Posashkova
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: revan1988@gmail.com

S. V. Posashkov
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: corlagon@univ.kiev.ua

DOI: http://dx.doi.org/10.1090/S0094-9000-2012-00845-4
PII: S 0094-9000(2012)00845-4
Keywords: Fractional Brownian motion, standard Brownian motion, stochastic differential equation, continuity in a parameter
Received by editor(s): May 28, 2010
Published electronically: February 2, 2012
Article copyright: © Copyright 2012 American Mathematical Society