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Slepian noise approach for Gaussian and Laplace moving average processes

Krys Podgorski ; Igor Rychlik (Institutionen för matematiska vetenskaper, matematisk statistik) ; Jonas Wallin (Institutionen för matematiska vetenskaper, matematisk statistik)
Extremes (1386-1999). Vol. 18 (2015), 4, p. 665-695.
[Artikel, refereegranskad vetenskaplig]

Slepian models are derived for a stochastic process observed at level crossings of a moving average driven by a gaussian or Laplace noise. In particular, a Slepian model for the noise – the Slepian noise – is developed. For Laplace moving average process a method of sampling from the Slepian noise is also obtained by a Gibbs sampler. This facilitates comparison of behavior at crossing of a level between a gaussian process and a non-gaussian one and allows to study a random processes sampled at crossings of a non-gaussian moving average process. In a numerical study based on the method it is observed that the behavior of a non-gaussian moving average process at high level crossings is fundamentally different from that for the gaussian case, which is in line with some recent theoretical results on the subject.

Nyckelord: Rice formula, Level crossings, Generalized Laplace distribution, Moving average process, Extreme episodes, Tilted Rayleigh distribution, Generalized inverse gaussian distribution



Denna post skapades 2015-11-06. Senast ändrad 2016-01-07.
CPL Pubid: 225336

 

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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematisk statistik (2005-2016)

Ämnesområden

Matematisk statistik

Chalmers infrastruktur