|
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
Posted:
February 2, 2012
Full-text PDF
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.
References
- 1.
D. Nualart and A. Răşcanu, Differential equation driven by fractional Brownian motion, Collect. Math. 53 (2002), no. 1, 55-81. MR 1893308 (2003f:60105)
- 2.
Yuliya S. Mishura, Stochastic calculus for fractional Brownian motion
and related processes, Lecture Notes in Mathematics, vol. 1929,
Springer-Verlag, Berlin, 2008. MR 2378138
(2008m:60064)
- 3.
Yu. S. Mishura and S. V. Posashkov, Existence and uniqueness of solution of mixed stochastic differential equation driven by fractional Brownian motion and Wiener process, Theory Stoch. Process. 29 (2007), 152-165. MR 2343820 (2009c:60158)
- 4.
S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional Integrals and Derivatives. Theory and Applications, Gordon and Breach Science Publishers, Yverdon, 1993. MR 1347689 (96d:26012)
- 5.
M. Zähle, Integration with respect to fractal functions and
stochastic calculus. I, Probab. Theory Related Fields
111 (1998), no. 3, 333–374. MR 1640795
(99j:60073), http://dx.doi.org/10.1007/s004400050171
Similar Articles
Retrieve articles in Theory of Probability and Mathematical Statistics
with MSC (2010):
60G22,
60H10
Retrieve articles in all journals
with MSC (2010):
60G22,
60H10
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):
28/MAY/2010
Posted:
February 2, 2012
Article copyright:
© Copyright 2012 American Mathematical Society
|
