MAGP (Maximum Analysis of Gaussian Processes). Numerical bounds for the distributions of the maxima of some one- and two-parameter Gaussian processes. We consider the class of real-valued stochastic processes indexed on a compact subset of ℝ or ℝ 2 with almost surely absolutely continuous sample paths. We obtain an implicit formula for the distributions of their maxima. The main result is the derivation of numerical bounds that turn out to be very accurate, in the Gaussian case, for levels that are not large. We also present the first explicit upper bound for the distribution tail of the maximum in the two-dimensional Gaussian framework. Numerical comparisons are performed with known tools such as the Rice upper bound and expansions based on the Euler characteristic. We deal numerically with the determination of the persistence exponent.
Keywords for this software
References in zbMATH (referenced in 7 articles , 1 standard article )
Showing results 1 to 7 of 7.
- Azaïs, Jean-Marc; Genz, Alan: Computation of the distribution of the maximum of stationary Gaussian processes (2013)
- Lindgren, Georg: Stationary stochastic processes. Theory and applications. (2013)
- Lindgren, G.: Slope distribution in front-back asymmetric stochastic Lagrange time waves (2010)
- Azaïs, Jean-Marc; Gassiat, Élisabeth; Mercadier, Cécile: The likelihood ratio test for general mixture models with or without structural parameter (2009)
- Azaïs, Jean-Marc; Wschebor, Mario: Level sets and extrema of random processes and fields. (2009)
- Åberg, Sofia: Wave intensities and slopes in Lagrangian seas (2007)
- Mercadier, Cécile: Numerical bounds for the distributions of the maxima of some one- and two-parameter Gaussian processes (2006)