Conditional sampling for max-stable processes with a mixed moving maxima representation. (English) Zbl 1312.60071
Summary: This paper deals with the question of conditional sampling and prediction for the class of stationary max-stable processes which allow for a mixed moving maxima representation. We develop an exact procedure for conditional sampling using the Poisson point process structure of such processes. For explicit calculations we restrict ourselves to the one-dimensional case and use a finite number of shape functions satisfying some regularity conditions. For more general shape functions, approximation techniques are presented. Our algorithm is applied to the Smith process and the Brown-Resnick process. Finally, we compare our computational results to other approaches. Here, the algorithm for Gaussian processes with transformed marginals turns out to be surprisingly competitive.
MSC:
| 60G70 | Extreme value theory; extremal stochastic processes |
| 62D05 | Sampling theory, sample surveys |
| 60G52 | Stable stochastic processes |
| 60G55 | Point processes (e.g., Poisson, Cox, Hawkes processes) |
Keywords:
max-stable processes; conditional sampling; extremes; mixed moving maxima; Poisson point processReferences:
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