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Journal Articles Electronic Communications in Probability Year : 2016

Increment stationarity of $L^2$-indexed stochastic processes: spectral representation and characterization

Abstract

We are interested in the increment stationarity property for $L^2$-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 [7], 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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Dates and versions

hal-01236156 , version 1 (01-12-2015)
hal-01236156 , version 2 (02-12-2016)

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Cite

Alexandre Richard. Increment stationarity of $L^2$-indexed stochastic processes: spectral representation and characterization. Electronic Communications in Probability, 2016, 21, pp.15. ⟨10.1214/16-ECP4727⟩. ⟨hal-01236156v2⟩
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