|
|
|---|
ISSN 1547-7363(online) ISSN 0094-9000(print)
Existence and uniqueness of the solution of a stochastic differential equation, driven by fractional Brownian motion with a stabilizing term
Authors:
Yu. S. Mishura and S. V. Posashkov
Translated by:
O. I. Klesov
Journal:
Theor. Probability and Math. Statist. 76 (2008), 131-139
MSC (2000):
Primary 60G15; Secondary 60H05, 60H10
DOI:
https://doi.org/10.1090/S0094-9000-08-00737-0
Published electronically:
July 16, 2008
MathSciNet review:
2368745
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: A stochastic differential equation driven by a Wiener process and fractional Brownian motion is considered in the paper. We prove the existence and uniqueness of the solution if the equation contains a certain stabilizing term.
- David Nualart and Aurel Răşcanu, Differential equations driven by fractional Brownian motion, Collect. Math. 53 (2002), no. 1, 55–81. MR 1893308
- Yuriy Krvavych and Yuliya Mishura, Exponential formula and Girsanov theorem for mixed semilinear stochastic differential equations, Mathematical finance (Konstanz, 2000) Trends Math., Birkhäuser, Basel, 2001, pp. 230–238. MR 1882834
- P. Cheridito, Regularizing Fractional Brownian Motion with a View towards Stock Price Modelling, Ph.D. Thesis, Swiss Federal Institute of Technology, Zurich, 2001.
- Masuyuki Hitsuda, Representation of Gaussian processes equivalent to Wiener process, Osaka Math. J. 5 (1968), 299–312. MR 243614
- I. I. Gikhman and A. V. Skorokhod, Stokhasticheskie differentsial′nye uravneniya i ikh prilozheniya, “Naukova Dumka”, Kiev, 1982 (Russian). MR 678374
Retrieve articles in Theory of Probability and Mathematical Statistics with MSC (2000): 60G15, 60H05, 60H10
Retrieve articles in all journals with MSC (2000): 60G15, 60H05, 60H10
Additional Information
Yu. S. Mishura
Affiliation:
Department of Probability Theory and Mathematical Statistics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue 6, Kyiv 03127, Ukraine
Email:
myus@univ.kiev.ua
S. V. Posashkov
Affiliation:
Department of Probability Theory and Mathematical Statistics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue 6, Kyiv 03127, Ukraine
Email:
corlagon@univ.kiev.ua
Keywords:
Stochastic differential equation,
existence and uniqueness of the solution,
fractional Brownian motion
Received by editor(s):
December 1, 2005
Published electronically:
July 16, 2008
Additional Notes:
The research of the first coauthor is partially supported by the NATO grant PST.CLG 890408
Article copyright:
© Copyright 2008
American Mathematical Society