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Article
The extremes of dependent chi-processes attracted by the Brown-Resnick process
Motivated by some recent works on the topic of the Brown-Resnick process, we study the functional limit theorem for normalized pointwise maxima of dependent chi-processes. It is proven that the properly normal...
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Article
Open AccessTactics analysis and evaluation of women football team based on convolutional neural network
In order to realize the process of player feature extraction and classification from multi-frequency frame-changing football match images more quickly, and complete the tactical plan that is more conducive to ...
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Article
Extremes of a Type of Locally Stationary Gaussian Random Fields with Applications to Shepp Statistics
Let \(\{Z(\tau ,s), (\tau ,s)\in [a,b]\times [0,T]\}\) { Z ( τ , s ) , ( τ , s ) ∈ [ a , b ] × [ 0 , T ] } with some positive constants a, b, T be a centered Gaussian random field with variance function $$...
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Article
Almost Sure Convergence for the Maximum of Nonstationary Random Fields
We obtain an almost sure limit theorem for the maximum of nonstationary random fields under some dependence conditions. The obtained result is applied to Gaussian random fields.
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Article
Maxima and sum for discrete and continuous time Gaussian processes
We study the asymptotic relation among the maximum of continuous weakly and strongly dependent stationary Gaussian process, the maximum of this process sampled at discrete time points, and the partial sum of t...
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Article
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
Limit laws for the maxima of stationary chi-processes under random index
Let \(\{\chi _{k}(t), t\ge 0\}\) { ...
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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
On Piterbarg Max-Discretisation Theorem for Standardised Maximum of Stationary Gaussian Processes
With motivation from Hüsler (Extremes 7:179–190, 2004) and Piterbarg (Extremes 7:161–177, 2004) in this paper we derive the joint limiting distribution of standardised maximum of a continuous, stationary Gaussian...
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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
Limit theorems for extremes of strongly dependent cyclo-stationary χ-processes
In this paper, with motivation from the paper of Konstant et al. (Lith Math J 44:196-208, 2004) we derive limit theorems for the maximum of strongly dependent cyclo-stationary
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Article
Exact tail asymptotics of the supremum of strongly dependent Gaussian processes over a random interval
Let \( \mathcal{T} \) be a positive random variable independent of a real-valued stochastic process ...
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Article
Some asymptotic results on extremes of incomplete samples
Let X 1,X 2, ⋯ be a sequence of independent and identically distributed random variables and M n = max {X 1,X ...
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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...
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Article
Almost sure central limit theorem for the maxima and sums of stationary Gaussian sequences
In this paper, we proved an almost sure central limit theorem for the maxima (after centered at the sample mean) and the partial sums of standardized stationary Gaussian sequences under some conditions related...
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Article
Almost sure central limit theorem for the products of U-statistics
Let (X n ) be a sequence of i.i.d random variables and U n a U-statistic corresponding to a s...
