Limit theorems for certain functionals associated with stable processes in Hölder space.

M. Ait Ouahra; Mohamed Eddahbi

Publicacions Matemàtiques (2001)

  • Volume: 45, Issue: 2, page 371-386
  • ISSN: 0214-1493

Abstract

top
In this paper we study the Hölder regularity property of the local time of a symmetric stable process of index 1 < α ≤ 2 and of its fractional derivative as a doubly indexed process with respect to the space and the time variables. As an application we establish some limit theorems for occupation times of one-dimensional symmetric stable processes in the space of Hölder continuous functions. Our results generalize those obtained by Fitzsimmons and Getoor for stable processes in the space on continuous functions. The limiting processes are fractional derivatives and Hilbert transforms of local times.

How to cite

top

Ait Ouahra, M., and Eddahbi, Mohamed. "Théorèmes limites pour certaines fonctionnelles associées aux processus stables sur l'espace de Hölder.." Publicacions Matemàtiques 45.2 (2001): 371-386. <http://eudml.org/doc/41434>.

@article{AitOuahra2001,
author = {Ait Ouahra, M., Eddahbi, Mohamed},
journal = {Publicacions Matemàtiques},
keywords = {Espacios de Hölder generalizados; Transformada de Hilbert; Procesos estocásticos; Funcionales; stable processes; local times},
language = {fre},
number = {2},
pages = {371-386},
title = {Théorèmes limites pour certaines fonctionnelles associées aux processus stables sur l'espace de Hölder.},
url = {http://eudml.org/doc/41434},
volume = {45},
year = {2001},
}

TY - JOUR
AU - Ait Ouahra, M.
AU - Eddahbi, Mohamed
TI - Théorèmes limites pour certaines fonctionnelles associées aux processus stables sur l'espace de Hölder.
JO - Publicacions Matemàtiques
PY - 2001
VL - 45
IS - 2
SP - 371
EP - 386
LA - fre
KW - Espacios de Hölder generalizados; Transformada de Hilbert; Procesos estocásticos; Funcionales; stable processes; local times
UR - http://eudml.org/doc/41434
ER -

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.