关于Brownian桥局部时间的存在性和Hölder正则性

IF 0.3 Q4 STATISTICS & PROBABILITY

Random Operators and Stochastic Equations Pub Date : 2022-10-26 DOI:10.1515/rose-2022-2087

O. Allaoui, A. Sghir, S. Hadiri

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引用次数: 0

摘要

摘要在本文中，我们将建立布朗桥的局部时间的存在性和Hölder正则性。我们的结果是通过使用[K.Es-Sebaiy，D.Nualart，Y.Ouknine和C.a.Tudor，与分数布朗运动相关的某些过程的占用密度，Stocurtics 82 2010，1-3133–147]中关于具有绝对连续随机漂移的高斯过程的Malliavin演算的结果获得的，结合Berman提出的基于高斯过程局部不确定性概念的经典方法[S.M.Berman，高斯过程的局部不确定性和局部时间，印第安纳大学数学杂志，1973/74，69–94]。

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

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].

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来源期刊

Random Operators and Stochastic Equations STATISTICS & PROBABILITY-

CiteScore

0.60

自引率

25.00%

发文量