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

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  • René L. Schilling

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).

Suggested Citation

  • René L. Schilling, 1998. "Feller Processes Generated by Pseudo-Differential Operators: On the Hausdorff Dimension of Their Sample Paths," Journal of Theoretical Probability, Springer, vol. 11(2), pages 303-330, April.
    • Handle: RePEc:spr:jotpro:v:11:y:1998:i:2:d:10.1023_a:1022678219821
    DOI: 10.1023/A:1022678219821
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    Cited by:

    1. Bo Li & Yimin Xiao & Xiaochuan Yang, 2019. "On the Favorite Points of Symmetric Lévy Processes," Journal of Theoretical Probability, Springer, vol. 32(4), pages 1943-1972, December.
    2. Kurt, Kevin & Frey, Rüdiger, 2022. "Markov-modulated affine processes," Stochastic Processes and their Applications, Elsevier, vol. 153(C), pages 391-422.
    3. Sebastian Rickelhoff & Alexander Schnurr, 2024. "The Time-Dependent Symbol of a Non-homogeneous Itô Process and Corresponding Maximal Inequalities," Journal of Theoretical Probability, Springer, vol. 37(3), pages 2508-2533, September.
    4. Xiaochuan Yang, 2018. "Hausdorff Dimension of the Range and the Graph of Stable-Like Processes," Journal of Theoretical Probability, Springer, vol. 31(4), pages 2412-2431, December.

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