Abstract
ABSTRACTLet X = {X(t)}t ⩾ 0 be an operator semistable Lévy process on with exponent E, where E is an invertible linear operator on . In this article, we determine exact Hausdorff measure functions for the range of X over the time interval [0, 1] under certain assumptions on the principal spectral component of E. As a byproduct, we also present Tauberian results for semistable subordinators and sharp bounds for the asymptotic behavior of the expected sojourn times of X.
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