Université Paris 6
Pierre et Marie Curie | Université Paris 7
Denis Diderot | |

CNRS U.M.R. 7599
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``Probabilités et Modèles Aléatoires''
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**Auteur(s): **

**Code(s) de Classification MSC:**

- 60J55 Local time and additive functionals
- 60J65 Brownian motion, See also {58G32}
- 60F05 Central limit and other weak theorems

**Résumé:** Fractional derivatives ${\cal D}^\gamma$ of Brownian
local times are well defined for all $\gamma<3/2$. We show that, in the weak
convergence sense, these fractional derivatives admit themselves derivatives
which feature all fractional Brownian motions. Strong approximation results
are also developed as counterparts of limit theorems for Brownian additive
functionals which feature the fractional derivatives of Brownian local
times.

**Mots Clés:** *Local time ; additive functional ; principal value ; Brownian sheet ; fractional Brownian motion ; Hilbert transform ; fractional
derivative*

**Date:** 1999-09-03

**Prépublication numéro:** *PMA-524*