Electronic Journal of Probability

The FBM Itô's Formula Through Analytic Continuation

D. Feyel and A. de La Pradelle

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Abstract

The Fractional Brownian Motion can be extended to complex values of the parameter $\alpha $ for $\Re\alpha \gt {1\over 2}$. This is a useful tool. Indeed, the obtained process depends holomorphically on the parameter, so that many formulas, as Itô formula, can be extended by analytic continuation. For large values of $\Re\alpha $, the stochastic calculus reduces to a deterministic one, so that formulas are very easy to prove. Hence they hold by analytic continuation for $\Re\alpha \le 1$, containing the classical case $\alpha =1$.

Article information

Source
Electron. J. Probab., Volume 6 (2001), paper no. 26, 22 pp.

Dates
Accepted: 1 October 2001
First available in Project Euclid: 19 April 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1461097656

Digital Object Identifier
doi:10.1214/EJP.v6-99

Mathematical Reviews number (MathSciNet)
MR1873303

Zentralblatt MATH identifier
1008.60074

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

Keywords
Wiener space Sobolev space Stochastic integral Fractional Brownian Motion Itô's formula

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Feyel, D.; de La Pradelle, A. The FBM Itô's Formula Through Analytic Continuation. Electron. J. Probab. 6 (2001), paper no. 26, 22 pp. doi:10.1214/EJP.v6-99. https://projecteuclid.org/euclid.ejp/1461097656


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