Domain and range symmetries of operator fractional Brownian fields

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An operator fractional Brownian field (OFBF) is a Gaussian, stationary increment Rn-valued random field on Rm that satisfies the operator self-similarity property {X(cEt)}t∈Rm=L{cHX(t)}t∈Rm, c>0, for two matrix exponents (E,H). In this paper, we characterize the domain and range symmetries of OFBF, respectively, as maximal groups with respect to equivalence classes generated by orbits and, based on a new anisotropic polar-harmonizable representation of OFBF, as intersections of centralizers. We also describe the sets of possible pairs of domain and range symmetry groups in dimensions (m,1) and (2,2).