Electronic Communications in Probability
- Electron. Commun. Probab.
- Volume 21 (2016), paper no. 31, 15 pp.
Increment stationarity of $L^2$-indexed stochastic processes: spectral representation and characterization
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 , 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.
Electron. Commun. Probab., Volume 21 (2016), paper no. 31, 15 pp.
Received: 20 November 2015
Accepted: 26 February 2016
First available in Project Euclid: 6 April 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60G10: Stationary processes 60G57: Random measures 60G60: Random fields 60G15: Gaussian processes 28C20: Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) [See also 46G12, 58C35, 58D20, 60B11]
Richard, Alexandre. Increment stationarity of $L^2$-indexed stochastic processes: spectral representation and characterization. Electron. Commun. Probab. 21 (2016), paper no. 31, 15 pp. doi:10.1214/16-ECP4727. https://projecteuclid.org/euclid.ecp/1459966700