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

DOI:
https://doi.org/10.1090/S0094-9000-2012-00845-4

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:
https://doi.org/10.1090/S0094-9000-2012-00845-4

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