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Path regularity for Feller semigroups via Gaussian kernel estimates and generalizations to arbitrary semigroups on C0

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Given γ ∈ (−1,1), we present a dyadic growth condition 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 Hölder spaces and in weighted Besov spaces of order γ. We show that, for operator semigroups satisfying Gaussian kernel estimates of order m>1, condition holds for all and even for all 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 mD.

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Correspondence to Sönke Blunck.

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Blunck, S. Path regularity for Feller semigroups via Gaussian kernel estimates and generalizations to arbitrary semigroups on C0. Probab. Theory Relat. Fields 133, 71–97 (2005). https://doi.org/10.1007/s00440-004-0415-2

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  • Assure
  • Growth Condition
  • Stochastic Process
  • Probability Theory
  • Mathematical Biology