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Extremes of Shepp statistics for fractional Brownian motion
Define the incremental fractional Brownian field with parameter H ∈ (0, 1) by Z H (τ, s) = B H
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Article
Open AccessA note on the almost sure central limit theorem for the product of some partial sums
Let ( X n ...
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Article
Almost sure asymptotics for extremes of non-stationary Gaussian random fields
In this paper, the authors prove an almost sure limit theorem for the maxima of non-stationary Gaussian random fields under some mild conditions related to the covariance functions of the Gaussian fields. As t...
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Article
Almost sure central limit theorem for partial sums of Markov chain
The authors prove an almost sure central limit theorem for partial sums based on an irreducible and positive recurrent Markov chain using logarithmic means, which realizes the extension of the almost sure cent...