Abstract. Let {X(t) : t ∈ R d } be a multivariate operator-self-similar random field with values in R m . Such fields were introduced in [24] and satisfy the scaling d in the Gaussian case. In particular, we enlighten the property that the Hausdorff dimension is determined by the real parts of the eigenvalues of E and D as well as the multiplicity of the eigenvalues of E.

We investigate the sample path regularity of multivariate operator-selfsimilar α-stable random fields with values in R m given by a harmonizable representation. Such fields were introduced in [25] as a generalization of both operatorself-similar stochastic processes and operator scaling random fields and satisfy the scaling propertyand D is a real m×m matrix. By using results in [8] we give an upper bound on the modulus of continuity. Based on this we determine the Hausdorff dimension of the sample paths. In particular, this solves an open problem in [25]. 1 2 ERCAN SÖNMEZ random fields [6,7]. Recall that a stochastic processwhereas a scalar valued random field {Y (t) : t ∈ R d } is said to be operator scaling of order E and some H > 0 ifNote that (E, D)-operator-self-similar random fields can be seen as an anisotropic generalization of an operator-self-similar random fieldThe theoretical importance of self-similar random fields has increased significantly during the past four decades. They are also useful to model various natural phenomena for instance in physics, geophysics, mathematical engineering, finance or internet traffic, see, e.g., [23,1,31,35,10,9,5,12,36]. A very important class of such fields is given by Gaussian random fields and, in particular, by fractional Brownian fields

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