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Existence and uniqueness of the solution of a stochastic differential equation, driven by fractional Brownian motion with a stabilizing term
Author(s):
Yu.
S.
Mishura;
S.
V.
Posashkov
Translated by:
O. I. Klesov
Original publication:
Teoriya Imovirnostei ta Matematichna Statistika,
vipusk 76
(2007).
Journal:
Theor. Probability and Math. Statist.
No. 76
(2008),
131-139.
MSC (2000):
Primary 60G15;
Secondary 60H05, 60H10
Posted:
July 16, 2008
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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:
-
- 1.
- D. Nualart and A. Răşcanu, Differential equations driven by fractional Brownian motion, Collection Mathematics 53 (2002), no. 1, 55-81. MR 1893308 (2003f:60105)
- 2.
- 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
- 3.
- P. Cheridito, Regularizing Fractional Brownian Motion with a View towards Stock Price Modelling, Ph.D. Thesis, Swiss Federal Institute of Technology, Zurich, 2001.
- 4.
- M. Hitsuda, Representation of Gaussian processes equivalent to Wiener process, Osaka J. Math. 5 (1968), 299-312. MR 0243614 (39:4935)
- 5.
- 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
DOI:
10.1090/S0094-9000-08-00737-0
PII:
S 0094-9000(08)00737-0
Keywords:
Stochastic differential equation,
existence and uniqueness of the solution,
fractional Brownian motion
Received by editor(s):
1/DEC/2005
Posted:
July 16, 2008
Additional Notes:
The research of the first coauthor is partially supported by the NATO grant PST.CLG 890408
Copyright of article:
Copyright
2008,
American Mathematical Society
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