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(cEt)}t∈Rm=L{cHX(t)}t∈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 Biermé et al. (2007).