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Theory of Probability and Mathematical Statistics
Theory of Probability and Mathematical Statistics
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
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 76 (2007).
Journal: Theor. Probability and Math. Statist. 76 (2008), 131-139
MSC (2000): Primary 60G15; Secondary 60H05, 60H10
Published electronically: July 16, 2008
MathSciNet review: 2368745
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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.


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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: http://dx.doi.org/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): 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