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The law of iterated logarithm for additive functionals and martingale additive functionals of Harris recurrent Markov processes

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  • Löcherbach, Eva
  • Loukianova, Dasha

Abstract

We use Nummelin splitting in continuous time in order to prove laws of iterated logarithm for additive functionals of a Harris recurrent Markov process, with deterministic or random renormalization.

Suggested Citation

  • Löcherbach, Eva & Loukianova, Dasha, 2009. "The law of iterated logarithm for additive functionals and martingale additive functionals of Harris recurrent Markov processes," Stochastic Processes and their Applications, Elsevier, vol. 119(7), pages 2312-2335, July.
    • Handle: RePEc:eee:spapps:v:119:y:2009:i:7:p:2312-2335
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    References listed on IDEAS

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    1. R. Höpfner & Yu. Kutoyants, 2003. "On a Problem of Statistical Inference in Null Recurrent Diffusions," Statistical Inference for Stochastic Processes, Springer, vol. 6(1), pages 25-42, January.
    2. Löcherbach, Eva & Loukianova, Dasha, 2008. "On Nummelin splitting for continuous time Harris recurrent Markov processes and application to kernel estimation for multi-dimensional diffusions," Stochastic Processes and their Applications, Elsevier, vol. 118(8), pages 1301-1321, August.
    3. Csáki, Endre & Földes, Antónia & Hu, Yueyun, 2004. "Strong approximations of additive functionals of a planar Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 109(2), pages 263-293, February.
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    Cited by:

    1. Yiran Liu & Harsha Honnappa & Samy Tindel & Nung Kwan Yip, 2021. "Infinite server queues in a random fast oscillatory environment," Queueing Systems: Theory and Applications, Springer, vol. 98(1), pages 145-179, June.
    2. Eva Löcherbach & Dasha Loukianova, 2012. "Deviation Inequalities for Centered Additive Functionals of Recurrent Harris Processes Having General State Space," Journal of Theoretical Probability, Springer, vol. 25(1), pages 231-261, March.

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