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A law of the iterated logarithm for stable processes in random scenery

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  • Khoshnevisan, Davar
  • Lewis, Thomas M.

Abstract

We prove a law of the iterated logarithm for stable processes in a random scenery. The proof relies on the analysis of a new class of stochastic processes which exhibit long-range dependence.

Suggested Citation

  • Khoshnevisan, Davar & Lewis, Thomas M., 1998. "A law of the iterated logarithm for stable processes in random scenery," Stochastic Processes and their Applications, Elsevier, vol. 74(1), pages 89-121, May.
    • Handle: RePEc:eee:spapps:v:74:y:1998:i:1:p:89-121
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    References listed on IDEAS

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    1. Dabrowski, AndréR. & Dehling, Herold, 1988. "A Berry-Esséen theorem and a functional law of the iterated logarithm for weakly associated random vectors," Stochastic Processes and their Applications, Elsevier, vol. 30(2), pages 277-289, December.
    2. Burton, Robert M. & Dabrowski, AndréRobert & Dehling, Herold, 1986. "An invariance principle for weakly associated random vectors," Stochastic Processes and their Applications, Elsevier, vol. 23(2), pages 301-306, December.
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    Cited by:

    1. Wendler, Martin, 2016. "The sequential empirical process of a random walk in random scenery," Stochastic Processes and their Applications, Elsevier, vol. 126(9), pages 2787-2799.
    2. Csáki, Endre & Révész, Pál & Shi, Zhan, 2001. "A strong invariance principle for two-dimensional random walk in random scenery," Stochastic Processes and their Applications, Elsevier, vol. 92(2), pages 181-200, April.
    3. Chen, Xia & Rosen, Jay, 2010. "Large deviations and renormalization for Riesz potentials of stable intersection measures," Stochastic Processes and their Applications, Elsevier, vol. 120(9), pages 1837-1878, August.
    4. 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.
    5. Guillotin-Plantard, Nadine & Poisat, Julien, 2013. "Quenched central limit theorems for random walks in random scenery," Stochastic Processes and their Applications, Elsevier, vol. 123(4), pages 1348-1367.
    6. Csáki, Endre & König, Wolfgang & Shi, Zhan, 1999. "An embedding for the Kesten-Spitzer random walk in random scenery," Stochastic Processes and their Applications, Elsevier, vol. 82(2), pages 283-292, August.
    7. Révész, Pál & Shi, Zhan, 2000. "Strong approximation of spatial random walk in random scenery," Stochastic Processes and their Applications, Elsevier, vol. 88(2), pages 329-345, August.
    8. Deuschel, Jean-Dominique & Fukushima, Ryoki, 2019. "Quenched tail estimate for the random walk in random scenery and in random layered conductance," Stochastic Processes and their Applications, Elsevier, vol. 129(1), pages 102-128.
    9. Zhang, Li-Xin, 2001. "The strong approximation for the Kesten-Spitzer random walk," Statistics & Probability Letters, Elsevier, vol. 53(1), pages 21-26, May.
    10. N. Guillotin-Plantard, 2001. "Dynamic ℤ d -Random Walks in a Random Scenery: A Strong Law of Large Numbers," Journal of Theoretical Probability, Springer, vol. 14(1), pages 241-260, January.
    11. Thomas M. Lewis, 2001. "The Length of the Longest Head-Run in a Model with Long Range Dependence," Journal of Theoretical Probability, Springer, vol. 14(2), pages 357-378, April.

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