Feller Processes Generated by Pseudo-Differential Operators: On the Hausdorff Dimension of Their Sample Paths1

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Abstract

Let {Xt}t≥0 be a Feller process generated by a pseudo-differential operator whose symbol satisfies sup x ∈ ℝn |q (x, ξ)| ≤ c (1 + Ψ (ξ)) for some fixed continuous negative definite function ψ(ξ). The Hausdorff dimension of the set {Xt: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).

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