Abstract
Given γ ∈ (−1,1), we present a dyadic growth condition Open image in new window on the finite dimensional distributions of operator semigroups on C0(E which - for γ>0 and Feller semigroups - assures that the corresponding Feller process has paths in local Holder spaces and in weighted Besov spaces of order γ. We show that, for operator semigroups satisfying Gaussian kernel estimates of order m>1, condition Open image in new window holds for all Open image in new window and even for all Open image in new window in the case of Feller semigroups. Such Gaussian kernel estimates are typical for Feller semigroups on fractals of walk dimension m and for semigroups generated by elliptic operators on ℝD of order m≥D.
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