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An almost sure invariance principle for some classes of non-stationary mixing sequences

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  • Hafouta, Yeor

Abstract

In this note we (in particular) prove an almost sure invariance principle (ASIP) for non-stationary and uniformly bounded sequences of random variables which are exponentially fast ϕ-mixing. The obtained rate is of order o(Vn14+δ) for an arbitrary δ>0, where Vn is the variance of the underlying partial sums Sn. For certain classes of inhomogeneous Markov chains we also prove a vector-valued ASIP with similar rates.

Suggested Citation

  • Hafouta, Yeor, 2023. "An almost sure invariance principle for some classes of non-stationary mixing sequences," Statistics & Probability Letters, Elsevier, vol. 193(C).
    • Handle: RePEc:eee:stapro:v:193:y:2023:i:c:s0167715222002413
    DOI: 10.1016/j.spl.2022.109728
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    References listed on IDEAS

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    1. Shao, Qi-Man, 1993. "Almost sure invariance principles for mixing sequences of random variables," Stochastic Processes and their Applications, Elsevier, vol. 48(2), pages 319-334, November.
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