Abstract
In this paperweconsider a classic problem concerning the high excursion probabilities of a Gaussian random field f living on a compact set T. We develop efficient computational methods for the tail probabilities ℙ{supT f(t) > b}. For each positive ε, we present Monte Carlo algorithms that run in constant time and compute the probabilities with relative error ε for arbitrarily large b. The efficiency results are applicable to a large class of Hölder continuous Gaussian random fields. Besides computations, the change of measure and its analysis techniques have several theoretical and practical indications in the asymptotic analysis of Gaussian random fields.
Original language | English (US) |
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Pages (from-to) | 787-816 |
Number of pages | 30 |
Journal | Advances in Applied Probability |
Volume | 47 |
Issue number | 3 |
DOIs | |
State | Published - Sep 2015 |
Bibliographical note
Publisher Copyright:© 2015 Applied Probability Trust.
Keywords
- Efficiency
- Gaussian random field
- High-level excursion
- Monte Carlo
- Tail distribution