Article

Journal of Theoretical Probability

, Volume 11, Issue 2, pp 303-330

First online:

Feller Processes Generated by Pseudo-Differential Operators: On the Hausdorff Dimension of Their Sample Paths

  • René L. Schilling

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Abstract

Let {X t} t≥0 be a Feller process generated by a pseudo-differential operator whose symbol satisfiesÇ∈∝n|q(Ç,ξ)|≤c(1=ψ)(ξ)) for some fixed continuous negative definite function ψ(ξ). The Hausdorff dimension of the set {X t:t∈E}, E ⊂ [0, 1] is any analytic set, is a.s. bounded above by βψ dim E. βψ is the Blumenthal−Getoor upper index of the Levy Process associated with ψ(ξ).

Levy-type process Hausdorff dimension Feller semigroup pseudo-differential operator