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Hausdorff Dimension of the Range and the Graph of Stable-Like Processes

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  • Xiaochuan Yang

    (Michigan State University)

Abstract

We determine the Hausdorff dimension for the range of a class of pure jump Markov processes in $$\mathbb {R}^d$$ R d , which turns out to be random and depends on the trajectories of these processes. The key argument is carried out through the SDE representation of these processes. The method developed here also allows to compute the Hausdorff dimension for the graph.

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  • 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.
    • Handle: RePEc:spr:jotpro:v:31:y:2018:i:4:d:10.1007_s10959-017-0784-y
    DOI: 10.1007/s10959-017-0784-y
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    References listed on IDEAS

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    1. Fu, Zongfei & Li, Zenghu, 2010. "Stochastic equations of non-negative processes with jumps," Stochastic Processes and their Applications, Elsevier, vol. 120(3), pages 306-330, March.
    2. Knopova, V. & Schilling, R.L. & Wang, J., 2015. "Lower bounds of the Hausdorff dimension for the images of Feller processes," Statistics & Probability Letters, Elsevier, vol. 97(C), pages 222-228.
    3. 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.
    4. Rimas Norvaiša & Donna Mary Salopek, 2002. "Estimating the p-Variation Index of a Sample Function: An Application to Financial Data Set," Methodology and Computing in Applied Probability, Springer, vol. 4(1), pages 27-53, March.
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