Stochastic Processes with a Particular Type of Variograms

Ma, Chunsheng

doi:https://doi.org/10.1155/2007/61579

Journal of Electrical and Computer Engineering

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Research Letter | Open Access

Volume 2007 | Article ID 061579 | https://doi.org/10.1155/2007/61579

Stochastic Processes with a Particular Type of Variograms

Chunsheng Ma¹

Academic Editor: Antonio Napolitano

Received16 Aug 2007

Accepted22 Nov 2007

Published29 Jan 2008

Abstract

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.

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Copyright

Copyright © 2007 Chunsheng Ma. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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