The limit distribution of the maximum increment of a random walk with regularly varying jump size distribution

DOI10.3150/10-BEJ255zbMath1215.60018arXiv1011.5718MaRDI QIDQ627285

Thomas Mikosch, Alfredas Račkauskas

Publication date: 28 February 2011

Published in: Bernoulli (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1011.5718

zbMATH Keywords

regular variationextreme value theoryFréchet distributionpoint process convergenceBanach space valued random elementepidemic change pointmaximum increment of a random walk

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Extreme value theory; extremal stochastic processes (60G70) Sums of independent random variables; random walks (60G50)

Related Items (13)

Epidemic change tests for the mean of innovations of an AR(1) process ⋮ Testing mean changes by maximal ratio statistics ⋮ On the asymptotic distribution of the scan statistic for empirical distributions ⋮ Testing epidemic change in nearly nonstationary process with statistics based on residuals ⋮ On Bernstein–Kantorovich invariance principle in Hölder spaces and weighted scan statistics ⋮ Convergence of \(U\)-processes in Hölder spaces with application to robust detection of a changed segment ⋮ The limit distribution of the maximum increment of a random walk with dependent regularly varying jump sizes ⋮ On the asymptotic of the maximal weighted increment of a random walk with regularly varying jumps: the boundary case ⋮ Holderian weak invariance principle for stationary mixing sequences ⋮ Extremes of the standardized Gaussian noise ⋮ Two-stage data segmentation permitting multiscale change points, heavy tails and dependence ⋮ Limiting distribution for the maximal standardized increment of a random walk ⋮ Asymptotic independence of three statistics of maximal segmental scores

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