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On limit theorems of some extensions of fractional Brownian motion and their additive functionals

M. Ait Ouahra

Faculté des Sciences, Laboratoire de Modélisation Stochastique, et Déterministe et URAC 04, Oujda, BP, 717, Maroc

E-mail Address: m.aitouahra@ump.ma

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S. Moussaten

Faculté des Sciences, Laboratoire de Modélisation Stochastique, et Déterministe et URAC 04, Oujda, BP, 717, Maroc

E-mail Address: s.moussaten@ump.ac.ma

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A. Sghir

Faculté des Sciences Meknès, Département de Mathématiques et Informatique, BP, 11201, Zitoune, Maroc

E-mail Address: sghir.aissa@gmail.com

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https://doi.org/10.1142/S0219493717500228Cited by:1 (Source: Crossref)

Abstract

This paper is divided into two parts. The first deals with some limit theorems to certain extensions of fractional Brownian motion like: bifractional Brownian motion, subfractional Brownian motion and weighted fractional Brownian motion. In the second part we give the similar results of their continuous additive functionals; more precisely, local time and its fractional derivatives involving slowly varying function.

Keywords:

AMSC: 60G18, 60J55, 60F05

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