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Moderate deviations for martingales and mixing random processes

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  • Gao, Fu-Qing

Abstract

We obtain a moderately large deviation theorem for martingales. Then this result is applied to prove that the empirical measures of a stationary [empty set][combining character]-mixing sequence of random variables satisfy moderately large deviation principle when [Sigma]+[infinity]n=1 [empty set][combining character](n)

Suggested Citation

  • Gao, Fu-Qing, 1996. "Moderate deviations for martingales and mixing random processes," Stochastic Processes and their Applications, Elsevier, vol. 61(2), pages 263-275, February.
    • Handle: RePEc:eee:spapps:v:61:y:1996:i:2:p:263-275
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    Citations

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    Cited by:

    1. Ma, Xiaocui & Xi, Fubao, 2017. "Moderate deviations for neutral stochastic differential delay equations with jumps," Statistics & Probability Letters, Elsevier, vol. 126(C), pages 97-107.
    2. Xiequan Fan & Ion Grama & Quansheng Liu, 2020. "Cramér Moderate Deviation Expansion for Martingales with One-Sided Sakhanenko’s Condition and Its Applications," Journal of Theoretical Probability, Springer, vol. 33(2), pages 749-787, June.
    3. Xue, Xiaofeng, 2021. "Moderate deviations of density-dependent Markov chains," Stochastic Processes and their Applications, Elsevier, vol. 140(C), pages 49-80.
    4. Chen, Lei & Gao, Fuqing, 2013. "Moderate deviation principle for Brownian motions on the unit sphere in Rd," Statistics & Probability Letters, Elsevier, vol. 83(11), pages 2486-2491.
    5. Benoist, Tristan & Fatras, Jan-Luka & Pellegrini, Clément, 2023. "Limit theorems for quantum trajectories," Stochastic Processes and their Applications, Elsevier, vol. 164(C), pages 288-310.
    6. Fan, Xiequan & Grama, Ion & Liu, Quansheng & Shao, Qi-Man, 2020. "Self-normalized Cramér type moderate deviations for stationary sequences and applications," Stochastic Processes and their Applications, Elsevier, vol. 130(8), pages 5124-5148.
    7. Ulrich Horst & Jan Wezelburger, 2006. "Non-ergodic Behavior in a Financial Market with Interacting Investors," 2006 Meeting Papers 229, Society for Economic Dynamics.
    8. I. G. Grama & E. Haeusler, 2006. "An Asymptotic Expansion for Probabilities of Moderate Deviations for Multivariate Martingales," Journal of Theoretical Probability, Springer, vol. 19(1), pages 1-44, January.
    9. Zhu, Lingjiong, 2013. "Moderate deviations for Hawkes processes," Statistics & Probability Letters, Elsevier, vol. 83(3), pages 885-890.

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