Translator Disclaimer
2012 Multiparameter processes with stationary increments: Spectral representation and integration
Andreas Basse-O'Connor, Svend-Erik Graversen, Jan Pedersen
Author Affiliations +
Electron. J. Probab. 17: 1-21 (2012). DOI: 10.1214/EJP.v17-2287

Abstract

In this article, a class of multiparameter processes with wide-sense stationary increments is studied. The content is as follows. (1) The spectral representation is derived; in particular, necessary and sufficient conditions for a measure to be a spectral measure is given. The relations to a commonly used class of processes, studied e.g. by Yaglom, is discussed. (2) Some classes of deterministic integrands, here referred to as predomains, are studied in detail. These predomains consist of functions or, more generally, distributions. Necessary and sufficient conditions for completeness of the predomains are given. (3) In a framework covering the classical Walsh-Dalang theory of a temporal-spatial process which is white in time and colored in space, a class of predictable integrands is considered. Necessary and sufficient conditions for completeness of the class are given, and this property is linked to a certain martingale representation property.

Citation

Download Citation

Andreas Basse-O'Connor. Svend-Erik Graversen. Jan Pedersen. "Multiparameter processes with stationary increments: Spectral representation and integration." Electron. J. Probab. 17 1 - 21, 2012. https://doi.org/10.1214/EJP.v17-2287

Information

Accepted: 5 September 2012; Published: 2012
First available in Project Euclid: 4 June 2016

zbMATH: 1260.60089
MathSciNet: MR2968681
Digital Object Identifier: 10.1214/EJP.v17-2287

Subjects:
Primary: 60G51
Secondary: 60G12, 60H05

JOURNAL ARTICLE
21 PAGES


SHARE
Vol.17 • 2012
Back to Top