STOCHASTIC STRATONOVICH CALCULUS fBm FOR FRACTIONAL BROWNIAN MOTION WITH HURST PARAMETER LESS THAN 1/2

STOCHASTIC STRATONOVICH CALCULUS fBm FOR FRACTIONAL BROWNIAN MOTION WITH HURST PARAMETER LESS THAN 1/2

In this paper we introduce a Stratonovich type stochastic integral with respect to the fractional Brownian motion with Hurst parameter less than 1/2. Using the techniques of the Malliavin calculus, we provide sufficient conditions for a process to be integrable. We deduce an Ito formula and we apply...

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Bibliographic Details
Published in:Taiwanese journal of mathematics Vol. 5; no. 3; pp. 609 - 632
Main Authors: Alòs, E., León, J. A., Nualart, D.
Format: Journal Article
Language:English
Published: Mathematical Society of the Republic of China (Taiwan) 01-09-2001
Subjects:
Brownian motion
Calculus
Covariance
Differential equations
Mathematical integrals
Mathematical integration
Perceptron convergence procedure
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Summary:In this paper we introduce a Stratonovich type stochastic integral with respect to the fractional Brownian motion with Hurst parameter less than 1/2. Using the techniques of the Malliavin calculus, we provide sufficient conditions for a process to be integrable. We deduce an Ito formula and we apply these results to study stochastic differential equations driven by a fractional Brownian motion with Hurst parameter less than 1/2.
ISSN:1027-5487
2224-6851
DOI:10.11650/twjm/1500574954