On integral representations of operator fractional Brownian fields
Probability
2014-05-26 v2 Statistics Theory
Statistics Theory
Abstract
Operator fractional Brownian fields (OFBFs) are Gaussian, stationary-increment vector random fields that satisfy the operator self-similarity relation {X(c^{E}t)}_{t in R^m} L= {c^{H}X(t)}_{t in R^m}. We establish a general harmonizable representation (Fourier domain stochastic integral) for OFBFs. Under additional assumptions, we also show how the harmonizable representation can be reexpressed as a moving average stochastic integral, thus answering an open problem described in Bierme et al.(2007), "Operator scaling stable random fields", Stochastic Processes and their Applications 117, 312--332.
Keywords
Cite
@article{arxiv.1403.6179,
title = {On integral representations of operator fractional Brownian fields},
author = {Changryong Baek and Gustavo Didier and Vladas Pipiras},
journal= {arXiv preprint arXiv:1403.6179},
year = {2014}
}