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- Title
EXTREMES OF HOMOGENEOUS GAUSSIAN RANDOM FIELDS.
- Authors
DĘBICKI, KRZYSZTOF; HASHORVA, ENKELEJD; SOJA-KUKIEłA, NATALIA
- Abstract
Let {X(s, t): s,t ≥ 0} be a centred homogeneous Gaussian field with almost surely continuous sample paths and correlation function r(s, t) = cov(X(s, t), X(0, 0)) such that ..., s, t → 0, with α1, α2 € (0, 2], and r(s, t) < 1 for (s, t) ≠ (0, 0). In this contribution we derive an asymptotic expansion (as u → ∞) of ... where ... which holds uniformly for (x, y) ∈ [A, B]² with A, B two positive constants and ψ the survival function of an N(0, 1) random variable. We apply our findings to the analysis of extremes of homogeneous Gaussian fields over more complex parameter sets and a ball of random radius. Additionally, we determine the extremal index of the discretised random field determined by X (s, t).
- Subjects
HOMOGENEOUS spaces; GAUSSIAN processes; RANDOM fields; ASYMPTOTIC expansions; PARAMETER estimation
- Publication
Journal of Applied Probability, 2015, Vol 52, Issue 1, p55
- ISSN
0021-9002
- Publication type
Article