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2012 A set-indexed Ornstein-Uhlenbeck process
Paul Balança, Erick Herbin
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Electron. Commun. Probab. 17: 1-14 (2012). DOI: 10.1214/ECP.v17-1903

Abstract

The purpose of this article is a set-indexed extension of the well known Ornstein-Uhlenbeck process. The first part is devoted to a stationary definition of the random field and ends up with the proof of a complete characterization by its $L^2$-continuity, stationarity and set-indexed Markov properties. This specific Markov transition system allows to define a general set-indexed Ornstein Uhlenbeck (SIOU) process with any initial probability measure. Finally, in the multiparameter case, the SIOU process is proved to admit a natural integral representation.

Citation

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Paul Balança. Erick Herbin. "A set-indexed Ornstein-Uhlenbeck process." Electron. Commun. Probab. 17 1 - 14, 2012. https://doi.org/10.1214/ECP.v17-1903

Information

Accepted: 5 September 2012; Published: 2012
First available in Project Euclid: 7 June 2016

zbMATH: 1266.60066
MathSciNet: MR2970703
Digital Object Identifier: 10.1214/ECP.v17-1903

Subjects:
Primary: 60G10
Secondary: 60G15, 60G60, 60J25

JOURNAL ARTICLE
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