Itô's formula with respect to fractional Brownian motion and its application.
Dai, W., Heyde, C.C. (1996)
Journal of Applied Mathematics and Stochastic Analysis
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Dai, W., Heyde, C.C. (1996)
Journal of Applied Mathematics and Stochastic Analysis
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David Nualart (2006)
Annales de la faculté des sciences de Toulouse Mathématiques
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Fractional Brownian motion (fBm) is a centered self-similar Gaussian process with stationary increments, which depends on a parameter called the Hurst index. In this conference we will survey some recent advances in the stochastic calculus with respect to fBm. In the particular case , the process is an ordinary Brownian motion, but otherwise it is not a semimartingale and Itô calculus cannot be used. Different approaches have been introduced to construct stochastic integrals with...
Constantin Tudor, Maria Tudor (2007)
Open Mathematics
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Patrick Cheridito, David Nualart (2005)
Annales de l'I.H.P. Probabilités et statistiques
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David Nualart, Aurel Rascanu (2002)
Collectanea Mathematica
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A global existence and uniqueness result of the solution for multidimensional, time dependent, stochastic differential equations driven by a fractional Brownian motion with Hurst parameter H > 1/2 is proved. It is shown, also, that the solution has finite moments. The result is based on a deterministic existence and uniqueness theorem whose proof uses a contraction principle and a priori estimates.
Zdzisław Brzeźniak, Jan van Neerven, Donna Salopek (2012)
Czechoslovak Mathematical Journal
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Let be a Hilbert space and a Banach space. We set up a theory of stochastic integration of -valued functions with respect to -cylindrical Liouville fractional Brownian motion with arbitrary Hurst parameter . For we show that a function is stochastically integrable with respect to an -cylindrical Liouville fractional Brownian motion if and only if it is stochastically integrable with respect to an -cylindrical fractional Brownian motion. We apply our results to stochastic...