B1487
Title: Slepian models for moving averages driven by a non-Gaussian noise
Authors: Krzysztof Podgorski - Lund University (Sweden) [presenting]
Jonas Wallin - Lund University (Sweden)
Igor Rychlik - Chalmers University (Sweden)
Abstract: Slepian models are derived describing the distributional form of a stochastic process observed at level crossings of a moving average driven by a Laplace noise. The approach is through a Gibbs sampler of a Slepian model for the Laplace noise. It allows for simultaneously studying a number of stochastic characteristics observed at the level crossing instants. A method of sampling from the corresponding biased sampling distribution of the underlying gamma process is also obtained from the same Gibbs sampler. This is used for efficient simulations of the behaviour of random processes sampled at crossings of a non-Gaussian moving average process. In particular, it facilitates comparisons of the behaviour when a Gaussian process and a non-Gaussian process are crossing a level. It is observed that the behaviour of the process at high-level crossings is fundamentally different from that in the Gaussian case, which is in line with some theoretical results on the subject.
