Electronic Journal of Probability
- Electron. J. Probab.
- Volume 8 (2003), paper no. 14, 31 p.
Itô Formula and Local Time for the Fractional Brownian Sheet
Ciprian Tudor and Frederi Viens
Abstract
Using the techniques of the stochastic calculus of variations for Gaussian processes, we derive an Itô formula for the fractional Brownian sheet with Hurst parameters bigger than $1/2$. As an application, we give a stochastic integral representation for the local time of the fractional Brownian sheet.
Article information
Source
Electron. J. Probab., Volume 8 (2003), paper no. 14, 31 p.
Dates
First available in Project Euclid: 23 May 2016
Permanent link to this document
https://projecteuclid.org/euclid.ejp/1464037587
Digital Object Identifier
doi:10.1214/EJP.v8-155
Mathematical Reviews number (MathSciNet)
MR1998763
Zentralblatt MATH identifier
1067.60030
Subjects
Primary: 60H07: Stochastic calculus of variations and the Malliavin calculus
Secondary: 60G18: Self-similar processes 60G15: Gaussian processes 60J55: Local time and additive functionals
Keywords
fractional Brownian sheet Ito formula local time Tanaka formula Malliavin calculus
Citation
Tudor, Ciprian; Viens, Frederi. Itô Formula and Local Time for the Fractional Brownian Sheet. Electron. J. Probab. 8 (2003), paper no. 14, 31 p. doi:10.1214/EJP.v8-155. https://projecteuclid.org/euclid.ejp/1464037587