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On Moduli of Continuity for Local Times of Fractional Stable Processes

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  • Raby Guerbaz

    (Hassan II University Mohammedia)

Abstract

We establish estimates for moduli of continuity of the local times of a class of self-similar stable processes. Our arguments yield also sharp lower bounds for the Hausdorff measure of the level sets of these processes. Finally, we prove the continuity in law of the local times with respect to the self-similarity index for a wide class of self-similar stable processes.

Suggested Citation

  • Raby Guerbaz, 2009. "On Moduli of Continuity for Local Times of Fractional Stable Processes," Journal of Theoretical Probability, Springer, vol. 22(4), pages 934-954, December.
    • Handle: RePEc:spr:jotpro:v:22:y:2009:i:4:d:10.1007_s10959-009-0214-x
    DOI: 10.1007/s10959-009-0214-x
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    References listed on IDEAS

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    1. Maria Jolis & Noèlia Viles, 2007. "Continuity in Law with Respect to the Hurst Parameter of the Local Time of the Fractional Brownian Motion," Journal of Theoretical Probability, Springer, vol. 20(2), pages 133-152, June.
    2. Dozzi, Marco & Soltani, A. Reza, 1997. "Local time for stable moving average processes: Hölder conditions," Stochastic Processes and their Applications, Elsevier, vol. 68(2), pages 195-207, June.
    3. Jolis, Maria & Viles, Noèlia, 2007. "Continuity with respect to the Hurst parameter of the laws of the multiple fractional integrals," Stochastic Processes and their Applications, Elsevier, vol. 117(9), pages 1189-1207, September.
    Full references (including those not matched with items on IDEAS)

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