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

Yeor Hafouta

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arXiv · 2005.02915

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

Yeor Hafouta

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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 $\phi$-mixing. The obtained rate is of order $o(V_n^{\frac14+\del})$ for an arbitrary $\del>0$, where $V_n$ is the variance of the underlying partial sums $S_n$. For certain classes of inhomogeneous Markov chains we also prove a vector-valued ASIP with similar rates.

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Yeor Hafouta. 2020-05-06. An almost sure invariance principle for some classes of non-stationary mixing sequences. https://arxiv.org/abs/2005.02915

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