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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