IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v74y1998i1p89-121.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(97)00105-1
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. Zhang, Li-Xin, 2001. "The strong approximation for the Kesten-Spitzer random walk," Statistics & Probability Letters, Elsevier, vol. 53(1), pages 21-26, May.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Zhang, Li-Xin, 2001. "Strassen's law of the iterated logarithm for negatively associated random vectors," Stochastic Processes and their Applications, Elsevier, vol. 95(2), pages 311-328, October.
    2. Cai, Zongwu & Roussas, George G., 1998. "Kaplan-Meier Estimator under Association," Journal of Multivariate Analysis, Elsevier, vol. 67(2), pages 318-348, November.
    3. Kim, Tae-Sung & Ko, Mi-Hwa & Han, Kwang-Hee, 2008. "On the almost sure convergence for a linear process generated by negatively associated random variables in a Hilbert space," Statistics & Probability Letters, Elsevier, vol. 78(14), pages 2110-2115, October.
    4. Huang, Wen-Tao & Xu, Bing, 2002. "Some maximal inequalities and complete convergences of negatively associated random sequences," Statistics & Probability Letters, Elsevier, vol. 57(2), pages 183-191, April.
    5. R.M. Balan, 2003. "A Strong Invariance Principle for Associated Random Fields," RePAd Working Paper Series lrsp-TRS390, Département des sciences administratives, UQO.
    6. Vu T. N. Anh & Nguyen T. T. Hien & Le V. Thanh & Vo T. H. Van, 2021. "The Marcinkiewicz–Zygmund-Type Strong Law of Large Numbers with General Normalizing Sequences," Journal of Theoretical Probability, Springer, vol. 34(1), pages 331-348, March.
    7. Mi-Hwa Ko & Tae-Sung Kim & Kwang-Hee Han, 2009. "A Note on the Almost Sure Convergence for Dependent Random Variables in a Hilbert Space," Journal of Theoretical Probability, Springer, vol. 22(2), pages 506-513, June.
    8. Kim, Tae-Sung & Ko, Mi-Hwa, 2008. "A central limit theorem for the linear process generated by associated random variables in a Hilbert space," Statistics & Probability Letters, Elsevier, vol. 78(14), pages 2102-2109, October.
    9. Antoine Lerbet, 2023. "Statistical inference on stationary shot noise random fields," Statistical Inference for Stochastic Processes, Springer, vol. 26(3), pages 551-580, October.
    10. Shao, Qi-Man & Su, Chun, 1999. "The law of the iterated logarithm for negatively associated random variables," Stochastic Processes and their Applications, Elsevier, vol. 83(1), pages 139-148, September.
    11. Xin Guo & Zhao Ruan & Lingjiong Zhu, 2015. "Dynamics of Order Positions and Related Queues in a Limit Order Book," Papers 1505.04810, arXiv.org, revised Oct 2015.
    12. Thuan, Nguyen Tran & Quang, Nguyen Van, 2016. "Negative association and negative dependence for random upper semicontinuous functions, with applications," Journal of Multivariate Analysis, Elsevier, vol. 145(C), pages 44-57.
    13. Chen, Jia, 2008. "Asymptotics of kernel density estimators on weakly associated random fields," Statistics & Probability Letters, Elsevier, vol. 78(18), pages 3230-3237, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:spapps:v:74:y:1998:i:1:p:89-121. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.