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On the local limit theorems for linear sequences of lower psi-mixing Markov chains

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  • Peligrad, Magda
  • Sang, Hailin
  • Zhang, Na

Abstract

In this paper we investigate the local limit theorem for partial sums of linear sequences of the form Xj=∑i∈Zaiξj−i. Here (ai)i∈Z is a sequence of constants satisfying ∑i∈Zai2<∞ and (ξi)i∈Z are functions of a stationary Markov chain with mean zero and finite second moment. The Markov chain is assumed to satisfy one-sided lower psi-mixing condition.

Suggested Citation

  • Peligrad, Magda & Sang, Hailin & Zhang, Na, 2024. "On the local limit theorems for linear sequences of lower psi-mixing Markov chains," Statistics & Probability Letters, Elsevier, vol. 210(C).
    • Handle: RePEc:eee:stapro:v:210:y:2024:i:c:s0167715224000774
    DOI: 10.1016/j.spl.2024.110108
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    References listed on IDEAS

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    1. Timothy Fortune & Magda Peligrad & Hailin Sang, 2021. "A local limit theorem for linear random fields," Journal of Time Series Analysis, Wiley Blackwell, vol. 42(5-6), pages 696-710, September.
    2. Mallik, Atul & Woodroofe, Michael, 2011. "A Central Limit Theorem for linear random fields," Statistics & Probability Letters, Elsevier, vol. 81(11), pages 1623-1626, November.
    3. Bradley, Richard C., 1997. "Every "lower psi-mixing" Markov chain is "interlaced rho-mixing"," Stochastic Processes and their Applications, Elsevier, vol. 72(2), pages 221-239, December.
    4. Yeor Hafouta & Yuri Kifer, 2016. "A Nonconventional Local Limit Theorem," Journal of Theoretical Probability, Springer, vol. 29(4), pages 1524-1553, December.
    5. Wang, Qiying & Lin, Yan-Xia & Gulati, Chandra M., 2001. "Asymptotics for moving average processes with dependent innovations," Statistics & Probability Letters, Elsevier, vol. 54(4), pages 347-356, October.
    6. Peligrad, Magda & Sang, Hailin & Xiao, Yimin & Yang, Guangyu, 2022. "Limit theorems for linear random fields with innovations in the domain of attraction of a stable law," Stochastic Processes and their Applications, Elsevier, vol. 150(C), pages 596-621.
    Full references (including those not matched with items on IDEAS)

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