Limit theorems for certain functionals associated to stable processes in a Hölder space
type: Item
instance of: scholarly article
title: Limit theorems for certain functionals associated to stable processes in a Hölder space
zbMATH Open document ID: 0995.60037
DOI: 10.5565/PUBLMAT_45201_04
author: V. Pereyra
published in: Publicacions Matemàtiques
publication date: 2002-10-21T00:00:00Z
full work available at URL: https://eudml.org/doc/41434
review text: Let \(\{L_t^x : t\geq 0, x\in\mathbb R\}\) be the local time of an \(\alpha\)-Levy motion \((Z_t)_{t\geq 0}\) where \(1<\alpha\leq 2\). The aim of the present paper is to investigate \(L_t^x\) as function of the two variables \(t\) and \(x\) jointly. For example, a Hölder type estimate is proved for \((t,x)\to L_t^x\). Furthermore, the authors verify Hölder conditions for certain fractional derivatives of \(L_t^x\) (here the derivative is taken with respect to \(x\in\mathbb R\)). As a consequence, limits of some special functionals of the motion \((Z_t)_{t\geq 0}\) may be described by means of fractional derivatives of \(L_t^x\).
reviewed by: Werner Linde
Mathematics Subject Classification ID: 60F25
Mathematics Subject Classification ID: 60G52
zbMATH DE Number: 1740172
zbMATH Keywords: stable processes
zbMATH Keywords: local times
MaRDI profile type: Publication
OpenAlex ID: W2074071195
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description: scientific article; zbMATH DE number 1740172