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Functional limit theorems for the maxima of perturbed random walk and divergent perpetuities in the M 1-topology
Let ( ξ 1 , η 1 ), ( ξ 2 , η 2 ),… be a sequence of i.i.d. two-dimensional random vectors. In the earlier article Iksanov and Pilipenko (2014) weak...
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Extremes of Gaussian processes with smooth random expectation and smooth random variance
Let ξ ( t ), t ∈ [0, T ], T > 0, be a Gaussian stationary process with expectation 0 and variance 1, and let η ( t ) and μ ( t ) be other sufficiently smooth...
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Clustering of high values in random fields
The asymptotic results that underlie applications of extreme random fields often assume that the variables are located on a regular discrete grid,...
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Multivariate peaks over thresholds models
Multivariate peaks over thresholds modelling based on generalized Pareto distributions has up to now only been used in few and mostly two-dimensional...
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Conditional extreme value models: fallacies and pitfalls
Conditional extreme value models have been introduced by Heffernan and Resnick (Ann. Appl. Probab., 17 , 537–571,
2007 ) to describe the asymptotic... -
Extreme values of the uniform order 1 autoregressive processes and missing observations
We investigate partial maxima of the uniform A R (1) processes with parameter r ⩾ 2. Positively and negatively correlated processes are considered....
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Generalized Pickands constants and stationary max-stable processes
Pickands constants play a crucial role in the asymptotic theory of Gaussian processes. They are commonly defined as the limits of a sequence of...
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Hidden regular variation under full and strong asymptotic dependence
Data exhibiting heavy-tails in one or more dimensions is often studied using the framework of regular variation. In a multivariate setting this...
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On shape of high massive excursions of trajectories of Gaussian homogeneous fields
We consider the asymptotic behavior of the probability of “physical extremes” of a Gaussian field which means the probability of excursions above a...
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Some limit results on supremum of Shepp statistics for fractional Brownian motion
Define the incremental fractional Brownian field Z H ( τ , s ) = B H ( s + τ ) − B H ( s ), where B H ( s ) is a standard fractional Brownian motion with...
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Maxima and minima of independent and non-identically distributed bivariate Gaussian triangular arrays
In this paper, joint limit distributions of maxima and minima on independent and non-identically distributed bivariate Gaussian triangular arrays is...
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A Poisson process reparameterisation for Bayesian inference for extremes
A common approach to modelling extreme values is to consider the excesses above a high threshold as realisations of a non-homogeneous Poisson...
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A complete convergence theorem for stationary regularly varying multivariate time series
For a class of stationary regularly varying and weakly dependent multivariate time series (
X n ), we prove the so-called complete convergence result... -
Statistical post-processing of forecasts for extremes using bivariate brown-resnick processes with an application to wind gusts
To improve the forecasts of weather extremes, we propose a joint spatial model for the observations and the forecasts, based on a bivariate...
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Multivariate Regular Variation of Discrete Mass Functions with Applications to Preferential Attachment Networks
Regular variation of a multivariate measure with a Lebesgue density implies the regular variation of its density provided the density satisfies some...
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On consistency of the likelihood moment estimators for a linear process with regularly varying innovations
In 1975 James Pickands III showed that the excesses over a high threshold are approximatly Generalized Pareto distributed. Since then, a variety of...