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2001 The FBM Itô's Formula Through Analytic Continuation
D. Feyel, A. de La Pradelle
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Electron. J. Probab. 6: 1-22 (2001). DOI: 10.1214/EJP.v6-99

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 $\alpha =1$.

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D. Feyel. A. de La Pradelle. "The FBM Itô's Formula Through Analytic Continuation." Electron. J. Probab. 6 1 - 22, 2001. https://doi.org/10.1214/EJP.v6-99

Information

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

zbMATH: 1008.60074
MathSciNet: MR1873303
Digital Object Identifier: 10.1214/EJP.v6-99

Subjects:
Primary: 60H05
Secondary: 60H07

Keywords: fractional Brownian motion , Itô's formula , Sobolev space , stochastic integral , Wiener space

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Vol.6 • 2001
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