On integral representations of operator fractional Brownian fields

Operator fractional Brownian fields (OFBFs) are Gaussian, stationary-increment vector random fields that satisfy the operator self-similarity relation {X(c(E)t)}(t is an element of Rm) = (){c(H)X(t)}(t pound is an element of Rm). We establish a general harmonizable representation (Fourier domain stochastic integral) for OFBFs. Under additional assumptions, we also show how the harmonizable representation can be re-expressed as a moving average stochastic integral, thus answering an open problem described in Bierme et al. (2007). (C) 2014 Elsevier B.V. All rights reserved.