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Large deviations for some weakly dependent random processes

Author

Listed:
  • Burton, Robert M.
  • Dehling, Herold

Abstract

In this paper we compute large deviation probabilities for two classes of weakly dependent processes, moving averages of i.i.d. random variables and Poisson center cluster random measures.

Suggested Citation

  • Burton, Robert M. & Dehling, Herold, 1990. "Large deviations for some weakly dependent random processes," Statistics & Probability Letters, Elsevier, vol. 9(5), pages 397-401, May.
    • Handle: RePEc:eee:stapro:v:9:y:1990:i:5:p:397-401
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    Citations

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    Cited by:

    1. Sung, Soo Hak, 2009. "A note on the complete convergence of moving average processes," Statistics & Probability Letters, Elsevier, vol. 79(11), pages 1387-1390, June.
    2. Zhou, Xingcai, 2010. "Complete moment convergence of moving average processes under [phi]-mixing assumptions," Statistics & Probability Letters, Elsevier, vol. 80(5-6), pages 285-292, March.
    3. Jiang, Tiefeng & Rao, M. Bhaskara & Wang, Xiangchen, 1995. "Large deviations for moving average processes," Stochastic Processes and their Applications, Elsevier, vol. 59(2), pages 309-320, October.
    4. Federico Camerlenghi & Claudio Macci & Elena Villa, 2021. "Asymptotic behavior of mean density estimators based on a single observation: the Boolean model case," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(5), pages 1011-1035, October.
    5. Chen, Pingyan & Hu, Tien-Chung & Volodin, Andrei, 2009. "Limiting behaviour of moving average processes under [phi]-mixing assumption," Statistics & Probability Letters, Elsevier, vol. 79(1), pages 105-111, January.
    6. Barbe, Ph. & McCormick, W.P., 2010. "An extension of a logarithmic form of Cramér's ruin theorem to some FARIMA and related processes," Stochastic Processes and their Applications, Elsevier, vol. 120(6), pages 801-828, June.
    7. Liu, Xiangdong & Qian, Hangyong & Cao, Linqiu, 2015. "The Davis–Gut law for moving average processes," Statistics & Probability Letters, Elsevier, vol. 104(C), pages 1-6.
    8. Nyrhinen, Harri, 1995. "On the typical level crossing time and path," Stochastic Processes and their Applications, Elsevier, vol. 58(1), pages 121-137, July.
    9. Ghosh, Souvik & Samorodnitsky, Gennady, 2009. "The effect of memory on functional large deviations of infinite moving average processes," Stochastic Processes and their Applications, Elsevier, vol. 119(2), pages 534-561, February.
    10. Yun-xia, Li & Li-xin, Zhang, 2004. "Complete moment convergence of moving-average processes under dependence assumptions," Statistics & Probability Letters, Elsevier, vol. 70(3), pages 191-197, December.
    11. Ahmed, S. Ejaz & Antonini, Rita Giuliano & Volodin, Andrei, 2002. "On the rate of complete convergence for weighted sums of arrays of Banach space valued random elements with application to moving average processes," Statistics & Probability Letters, Elsevier, vol. 58(2), pages 185-194, June.
    12. Lovas, Attila & Rásonyi, Miklós, 2021. "Markov chains in random environment with applications in queuing theory and machine learning," Stochastic Processes and their Applications, Elsevier, vol. 137(C), pages 294-326.
    13. Zhang, Li-Xin, 1996. "Complete convergence of moving average processes under dependence assumptions," Statistics & Probability Letters, Elsevier, vol. 30(2), pages 165-170, October.
    14. Kim, Tae-Sung & Ko, Mi-Hwa, 2008. "Complete moment convergence of moving average processes under dependence assumptions," Statistics & Probability Letters, Elsevier, vol. 78(7), pages 839-846, May.
    15. Wenzhi Yang & Shuhe Hu & Xuejun Wang, 2012. "Complete Convergence for Moving Average Process of Martingale Differences," Discrete Dynamics in Nature and Society, Hindawi, vol. 2012, pages 1-16, July.
    16. Yun-Xia, Li, 2006. "Precise asymptotics in complete moment convergence of moving-average processes," Statistics & Probability Letters, Elsevier, vol. 76(13), pages 1305-1315, July.
    17. Jong-Il Baek & Sung-Tae Park, 2010. "RETRACTED ARTICLE: Convergence of Weighted Sums for Arrays of Negatively Dependent Random Variables and Its Applications," Journal of Theoretical Probability, Springer, vol. 23(2), pages 362-377, June.

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