Stochastic processes with a particular type of variograms
type: Item
instance of: scholarly article
title: Stochastic processes with a particular type of variograms
zbMATH Open document ID: 1214.60018
DOI: 10.1155/2007/61579
author: C. Ma
published in: Research Letters in Signal Processing
publication date: 2010-07-22T00:00:00Z
review text: Summary: This paper is concerned with a class of stochastic processes or random fields with second-order increments, whose variograms have a particular form, among which stochastic processes having orthogonal increments on the real line form an important subclass. A natural issue, how big this subclass is, has not been explicitly addressed in the literature. As a solution, this paper characterizes a stochastic process having orthogonal increments on the real line in terms of its variogram or its construction. Our findings are a little bit surprising: this subclass is big in terms of the variogram, and on the other hand, it is relatively ``small'' according to a simple construction. In particular, every such process with Gaussian increments can be simply constructed from Brownian motion. Using the characterizations we obtain a series expansion of the stochastic process with orthogonal increments.
Mathematics Subject Classification ID: 60G51
Mathematics Subject Classification ID: 60G12
zbMATH DE Number: 5759234
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2007/61579
OpenAlex ID: W1966195492
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description: scientific article; zbMATH DE number 5759234