Skip to Main content Skip to Navigation

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

* Corresponding author
1 TOSCA - TO Simulate and CAlibrate stochastic models
CRISAM - Inria Sophia Antipolis - Méditerranée , IECL - Institut Élie Cartan de Lorraine : UMR7502
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.
Keywords :
Document type :
Journal articles
Domain :
Complete list of metadata

Cited literature [21 references]

https://hal.inria.fr/hal-01236156
Contributor : Alexandre Richard <>
Submitted on : Friday, December 2, 2016 - 10:35:27 AM
Last modification on : Tuesday, May 18, 2021 - 2:32:02 PM
Long-term archiving on: : Tuesday, March 21, 2017 - 3:12:07 AM

### File

L2Stat.pdf
Files produced by the author(s)

### Citation

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

Record views

Files downloads