Stochastic Stratonovich calculus fBm for fractional Brownian motion with Hurst parameter less than 1/2

Authors
Alos, E Leon, JA Nualart, D
Citation
E. Alos et al., Stochastic Stratonovich calculus fBm for fractional Brownian motion with Hurst parameter less than 1/2, TAIWAN J M, 5(3), 2001, pp. 609-632
Citations number
24
Categorie Soggetti
Mathematics
Journal title
TAIWANESE JOURNAL OF MATHEMATICS
ISSN journal
10275487 → ACNP
Volume
5
Issue
3
Year of publication
2001
Pages
609 - 632
Database
ISI
SICI code
1027-5487(200109)5:3<609:SSCFFF>2.0.ZU;2-X
Abstract
In this paper we introduce a Stratonovich type stochastic integral with res pect to the fractional Brownian motion with Hurst parameter less than 1/2. Using the techniques of the Malliavin calculus, we provide sufficient condi tions for a process to be integrable. We deduce an Ito formula and we apply these results to study stochastic differential equations driven by a fract ional Brownian motion with Hurst parameter less than 1/2.