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
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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.
References
- 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.
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References
- D. Nualart and A. Răşcanu, Differential equations driven by fractional Brownian motion, Collection Mathematics 53 (2002), no. 1, 55–81. MR 1893308 (2003f:60105)
- Yu. Krvavych and Yu. Mishura, Exponential formula and Girsanov theorem for mixed semilinear stochastic differential equations, Mathematical Finance (Trends in Mathematics), 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.
- M. Hitsuda, Representation of Gaussian processes equivalent to Wiener process, Osaka J. Math. 5 (1968), 299–312. MR 0243614 (39:4935)
- I. I. Gikhman and A. V. Skorokhod, Stochastic Differential Equations and their Applications, “Naukova dumka”, Kiev, 1982. (Russian) MR 678374 (84j:60003)
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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
