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An operator fractional Brownian field (OFBF) is a Gaussian, stationaryincrement R^n-valued random field on R^m that satisfies the operatorself-similarity property {X(c^E t)}_{t in R^m} L= {c^H X(t)}_{t in R^m}, c > 0,for two matrix exponents (E,H). In this paper, we characterize the domain andrange symmetries of OFBF, respectively, as maximal groups with respect toequivalence classes generated by orbits and, based on a new anisotropicpolar-harmonizable representation of OFBF, as intersections of centralizers. Wealso describe the sets of possible pairs of domain and range symmetry groups indimensions (m,1) and (2,2).

Domain and range symmetries of operator fractional Brownian fields