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Maximal upper bounds for the moments of stochastic integrals and solutions of stochastic differential equations with respect to fractional Brownian motion with Hurst index  . I
Author(s):
Yu.
V.
Kozachenko;
Yu.
S.
Mishura
Translated by:
O. I. Klesov
Original publication:
Teoriya Imovirnostei ta Matematichna Statistika,
vipusk 75
(2006).
Journal:
Theor. Probability and Math. Statist.
No. 75
(2007),
51-64.
MSC (2000):
Primary 60G15, 60H05
Posted:
January 23, 2008
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Abstract:
Upper moment bounds and maximal upper moment bounds are obtained for Wiener integrals considered with respect to a fractional Brownian motion with Hurst index  . Maximal bounds are derived from new maximal inequalities for Gaussian random variables and stochastic processes.
References:
-
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- C. Bender, Integration with Respect to a Fractional Brownian Motion and Related Market Models, Ph.D. Thesis, Konstanz University, 2003.
- 3.
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Additional Information:
Yu.
V.
Kozachenko
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:
yvk@univ.kiev.ua
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
DOI:
10.1090/S0094-9000-08-00713-8
PII:
S 0094-9000(08)00713-8
Keywords:
Fractional Brownian motion,
Wiener integral,
moment inequalities,
Gaussian stochastic processes
Received by editor(s):
1/DEC/2005
Posted:
January 23, 2008
Additional Notes:
This work is partially supported by the NATO grant PST.CLG.980408
Copyright of article:
Copyright
2008,
American Mathematical Society
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