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Local times of additive Lévy processes

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  • Khoshnevisan, Davar
  • Xiao, Yimin
  • Zhong, Yuquan

Abstract

Let be an additive Lévy process in withwhere X1,...,XN are independent, classical Lévy processes on with Lévy exponents [Psi]1,...,[Psi]N, respectively. Under mild regularity conditions on the [Psi]i's, we derive moment estimates that imply joint continuity of the local times in question. These results are then refined to precise estimates for the local and uniform moduli of continuity of local times when all of the Xi's are strictly stable processes with the same index [alpha][set membership, variant](0,2].

Suggested Citation

  • Khoshnevisan, Davar & Xiao, Yimin & Zhong, Yuquan, 2003. "Local times of additive Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 104(2), pages 193-216, April.
    • Handle: RePEc:eee:spapps:v:104:y:2003:i:2:p:193-216
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    References listed on IDEAS

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    1. Vares, Maria E., 1983. "Local times for two-parameter Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 15(1), pages 59-82, June.
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    Cited by:

    1. Hyunchul Park & Yimin Xiao & Xiaochuan Yang, 2020. "Uniform Dimension Results for the Inverse Images of Symmetric Lévy Processes," Journal of Theoretical Probability, Springer, vol. 33(4), pages 2213-2232, December.
    2. Thomas S. Mountford, 2007. "Level Sets of Multiparameter Stable Processes," Journal of Theoretical Probability, Springer, vol. 20(1), pages 25-46, March.
    3. Chen, Xia, 2006. "Self-intersection local times of additive processes: Large deviation and law of the iterated logarithm," Stochastic Processes and their Applications, Elsevier, vol. 116(9), pages 1236-1253, September.

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