Slepian noise approach for Gaussian and Laplace moving average processes
Artikel i vetenskaplig tidskrift, 2015
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.
Moving average process
Generalized inverse gaussian distribution
Tilted Rayleigh distribution
Generalized Laplace distribution