On the existence and the Hölder regularity of the local time of the Brownian bridge-Reference-Cited by-同舟云学术

On the existence and the Hölder regularity of the local time of the Brownian bridge

Published:2022-10-26 Issue:4 Volume:30 Page:259-270
ISSN:0926-6364
Container-title:Random Operators and Stochastic Equations
language:en
Short-container-title:

Author:

Allaoui Omar¹,Sghir Aissa¹,Hadiri Soukaina²

Affiliation:

1. Department of Mathematics , Stochastic and Deterministic Modelling Laboratory (LAMSD), Faculty of Sciences Oujda Morocco , Mohamed First University , Oujda , Morocco

2. Department of Industrial Engineering , System Engineering and Decision Support Laboratory (LISAD), National School of Applied Sciences Agadir Morocco , Ibn Zohr University , Agadir , Morocco

Abstract

Abstract In this paper, we will establish the existence and the Hölder regularity of the local time of the Brownian bridge. Our results are obtained by using a result on Malliavin calculus in [K. Es-Sebaiy, D. Nualart, Y. Ouknine and C. A. Tudor, Occupation densities for certain processes related to fractional Brownian motion, Stochastics 82 2010, 1–3, 133–147] for a Gaussian process with an absolutely continuous random drift, jointly with the classical approach based on the concept of local nondeterminism for Gaussian processes introduced by Berman [S. M. Berman, Local nondeterminism and local times of Gaussian processes, Indiana Univ. Math. J. 23 1973/74, 69–94].

Publisher

Walter de Gruyter GmbH

Subject

Statistics and Probability,Analysis

Link

https://www.degruyter.com/document/doi/10.1515/rose-2022-2087/pdf

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