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On the Favorite Points of Symmetric Lévy Processes

Author

Listed:
  • Bo Li

    (Central China Normal University)

  • Yimin Xiao

    (Michigan State University)

  • Xiaochuan Yang

    (Michigan State University)

Abstract

This paper is concerned with asymptotic behavior (at zero and at infinity) of the favorite points of Lévy processes. By exploring Molchan’s idea for deriving lower tail probabilities of Gaussian processes with stationary increments, we extend the result of Marcus (J Theor Probab 14(3):867–885, 2001) on the favorite points to a larger class of symmetric Lévy processes.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jotpro:v:32:y:2019:i:4:d:10.1007_s10959-018-0857-6
    DOI: 10.1007/s10959-018-0857-6
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    References listed on IDEAS

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    1. 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.
    2. Berman, Simeon M., 1987. "Spectral conditions for local nondeterminism," Stochastic Processes and their Applications, Elsevier, vol. 27, pages 73-84.
    3. Shen, Yi, 2016. "Random locations, ordered random sets and stationarity," Stochastic Processes and their Applications, Elsevier, vol. 126(3), pages 906-929.
    4. Eisenbaum, Nathalie & Kaspi, Haya, 2009. "On permanental processes," Stochastic Processes and their Applications, Elsevier, vol. 119(5), pages 1401-1415, May.
    5. Michael B. Marcus, 2001. "The Most Visited Sites of Certain Lévy Processes," Journal of Theoretical Probability, Springer, vol. 14(3), pages 867-885, July.
    6. Eisenbaum, Nathalie & Khoshnevisan, Davar, 2002. "On the most visited sites of symmetric Markov processes," Stochastic Processes and their Applications, Elsevier, vol. 101(2), pages 241-256, October.
    Full references (including those not matched with items on IDEAS)

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