Taiwanese Journal of Mathematics

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

E. Alos, J. A. Leon, and D. Nualart

Full-text: Open access

Abstract

In this paper we introduce a Stratonovich type stochastic integralwith respect to the fractional Brownian motion with Hurst parameter less than1/2. Using the techniques of the Malliavin calculus, we provide sufficientconditions for a process to be integrable. We deduce an It^o formula andwe apply these results to study stochastic differential equations driven by afractional Brownian motion with Hurst parameter less than 1/2.

Article information

Source
Taiwanese J. Math., Volume 5, Number 3 (2001), 609-632.

Dates
First available in Project Euclid: 20 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500574954

Digital Object Identifier
doi:10.11650/twjm/1500574954

Mathematical Reviews number (MathSciNet)
MR1849782

Zentralblatt MATH identifier
0989.60054

Subjects
Primary: 60H05: Stochastic integrals 60H07: Stochastic calculus of variations and the Malliavin calculus

Keywords
stochastic calculus Stratonovich integral Malliavin calculus fractional Brownian motion stochastic differential equations

Citation

Alos, E.; Leon, J. A.; Nualart, D. STOCHASTIC STRATONOVICH CALCULUS fBm FOR FRACTIONAL BROWNIAN MOTION WITH HURST PARAMETER LESS THAN 1/2. Taiwanese J. Math. 5 (2001), no. 3, 609--632. doi:10.11650/twjm/1500574954. https://projecteuclid.org/euclid.twjm/1500574954


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