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Article Dans Une Revue Annals of Probability Année : 2003

Generalized covariations, local time and Stratonovich Itô's formula for fractional Brownian motion with Hurst index H>=1/4

Mihai Gradinaru
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Pierre Vallois

Résumé

Given a locally bounded real function g, we examine the existence of a 4-covariation $[g(B^H), B^H, B^H, B^H]$, where $B^H$ is a fractional Brownian motion with a Hurst index $H \ge \tfrac{1}{4}$. We provide two essential applications. First, we relate the 4-covariation to one expression involving the derivative of local time, in the case $H = \tfrac{1}{4}$, generalizing an identity of Bouleau--Yor type, well known for the classical Brownian motion. A second application is an Itô formula of Stratonovich type for $f(B^H)$. The main difficulty comes from the fact $B^H$ has only a finite 4-variation.
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Dates et versions

hal-00091324 , version 1 (05-09-2006)

Identifiants

Citer

Mihai Gradinaru, Francesco Russo, Pierre Vallois. Generalized covariations, local time and Stratonovich Itô's formula for fractional Brownian motion with Hurst index H>=1/4. Annals of Probability, 2003, 31, pp.1772-1820. ⟨10.1214/aop/1068646366⟩. ⟨hal-00091324⟩
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