A law of the iterated logarithm for stable processes in random scenery
type: Item
instance of: scholarly article
title: A law of the iterated logarithm for stable processes in random scenery
zbMATH Open document ID: 0932.60033
DOI: 10.1016/S0304-4149(97)00105-1
author: D. Khoshnevisan
author: Thomas M. Lewis
published in: Stochastic Processes and their Applications
publication date: 1999-11-18T00:00:00Z
review text: The goal of this article is to present deterministically normalized laws of the iterated logarithm for stable processes in random scenery and random walks in random scenery. The proof relies on the analysis of a new class of stochastic processes which exhibit long-range dependence. To overcome some difficulties, the authors introduce and study quasi-associated collections of random variables, which may be of independent interest and worthy of further examination. Another source of interest in stable processes in random scenery is motivated by some newly found connections between this process and iterated Brownian motion [the authors, ``Stochastic calculus for Brownian motion on a Brownian fracture'' (Preprint, 1966)].
Mathematics Subject Classification ID: 60G10
Mathematics Subject Classification ID: 60G15
Mathematics Subject Classification ID: 60G50
Mathematics Subject Classification ID: 60G52
zbMATH DE Number: 1364459
zbMATH Keywords: law of the iterated logarithm
zbMATH Keywords: random walk
zbMATH Keywords: random scenery
zbMATH Keywords: Brownian motion
zbMATH Keywords: quasi-association
zbMATH Keywords: Gaussian process
reviewed by: Gejza Dohnal
MaRDI profile type: Publication
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full work available at URL: s0304-4149(97)00105-1
OpenAlex ID: W1972975460
description: scientific article; zbMATH DE number 1364459