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Moderate deviations for Markovian occupation times

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  • Chen, Xia

Abstract

In this paper, we establish the moderate deviations for occupation times of Markov processes under the conditions given in Darling-Kac (1957. Trans. Amer. Math. Soc. 84, 444-458). When applied to the law of the iterated logarithm, our results generalize those obtained in Marcus-Rosen (1994a. Ann. Probab. 22, 626-658; 1994b. Ann. Inst. Henri Poincaré Probab. Statist. 30, 467-499) for Lévy processes and random walks, and those obtained recently by the author (1999. Ann. Probab. 27, 1324-1346) for Harris recurrent Markov chains.

Suggested Citation

  • Chen, Xia, 2001. "Moderate deviations for Markovian occupation times," Stochastic Processes and their Applications, Elsevier, vol. 94(1), pages 51-70, July.
    • Handle: RePEc:eee:spapps:v:94:y:2001:i:1:p:51-70
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    References listed on IDEAS

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    1. Fitzsimmons, P. J. & Pitman, Jim, 1999. "Kac's moment formula and the Feynman-Kac formula for additive functionals of a Markov process," Stochastic Processes and their Applications, Elsevier, vol. 79(1), pages 117-134, January.
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    Cited by:

    1. Gantert, Nina & van der Hofstad, Remco & König, Wolfgang, 2006. "Deviations of a random walk in a random scenery with stretched exponential tails," Stochastic Processes and their Applications, Elsevier, vol. 116(3), pages 480-492, March.
    2. Zhu, Lingjiong, 2013. "Moderate deviations for Hawkes processes," Statistics & Probability Letters, Elsevier, vol. 83(3), pages 885-890.
    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.

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