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2016 Increment stationarity of $L^2$-indexed stochastic processes: spectral representation and characterization
Alexandre Richard
Electron. Commun. Probab. 21: 1-15 (2016). DOI: 10.1214/16-ECP4727

Abstract

We are interested in the increment stationarity property of $L^2$-indexed stochastic processes, which is a fairly general concern since many random fields can be interpreted as the restriction of a more generally defined $L^2$-indexed process. We first give a spectral representation theorem in the sense of Ito [9], and see potential applications on random fields, in particular on the $L^2$-indexed extension of the fractional Brownian motion. Then we prove that this latter process is characterized by its increment stationarity and self-similarity properties, as in the one-dimensional case.

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Alexandre Richard. "Increment stationarity of $L^2$-indexed stochastic processes: spectral representation and characterization." Electron. Commun. Probab. 21 1 - 15, 2016. https://doi.org/10.1214/16-ECP4727

Information

Received: 20 November 2015; Accepted: 26 February 2016; Published: 2016
First available in Project Euclid: 6 April 2016

zbMATH: 1336.60073
MathSciNet: MR3485400
Digital Object Identifier: 10.1214/16-ECP4727

Subjects:
Primary: 28C20, 60G10, 60G15, 60G57, 60G60

JOURNAL ARTICLE
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