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 Electronic Journal of Probability > Vol. 6 (2001) > Paper 26 open journal systems 


The FBM Itô's Formula Through Analytic Continuation

D. Feyel, Université Evry
A. de La Pradelle, Université Paris VI


Abstract
The Fractional Brownian Motion can be extended to complex values of the parameter $alpha $ for $Realpha >{1over 2}$. 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 $Realpha $, the stochastic calculus reduces to a deterministic one, so that formulas are very easy to prove. Hence they hold by analytic continuation for $Realpha le 1$, containing the classical case $alpha =1$.


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Pages: 1-22

Published on: October 1, 2001
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Electronic Journal of Probability. ISSN: 1083-6489