On the Tail Probabilities of Aggregated Lognormal Random Fields with Small Noise

2016 ◽  
Vol 41 (1) ◽  
pp. 236-246 ◽  
Author(s):  
Xiaoou Li ◽  
Jingchen Liu ◽  
Gongjun Xu
Keyword(s):  
Random Fields ◽  
Tail Probabilities ◽  
Small Noise ◽  
Lognormal Random Fields

scholarly journals Rare-event simulation and efficient discretization for the supremum of Gaussian random fields

2015 ◽  
Vol 47 (03) ◽  
pp. 787-816
Author(s):  
Xiaoou Li ◽  
Jingchen Liu
Keyword(s):  
Random Fields ◽  
Gaussian Random Field ◽  
Rare Event ◽  
Gaussian Random Fields ◽  
Compact Set ◽  
Tail Probabilities ◽  
Hölder Continuous ◽  
Event Simulation ◽  
Classic Problem ◽  
Monte Carlo Algorithms

In this paper we consider a classic problem concerning the high excursion probabilities of a Gaussian random fieldfliving on a compact setT. We develop efficient computational methods for the tail probabilitiesℙ{supTf(t) >b}. For each positive ε, we present Monte Carlo algorithms that run inconstanttime and compute the probabilities with relative error ε for arbitrarily largeb. 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.

scholarly journals Rare-event simulation and efficient discretization for the supremum of Gaussian random fields

2015 ◽  
Vol 47 (3) ◽  
pp. 787-816 ◽  
Author(s):  
Xiaoou Li ◽  
Jingchen Liu
Keyword(s):  
Random Fields ◽  
Gaussian Random Field ◽  
Rare Event ◽  
Gaussian Random Fields ◽  
Compact Set ◽  
Tail Probabilities ◽  
Hölder Continuous ◽  
Event Simulation ◽  
Classic Problem ◽  
Monte Carlo Algorithms

In this paper we consider a classic problem concerning the high excursion probabilities of a Gaussian random fieldfliving on a compact setT. We develop efficient computational methods for the tail probabilitiesℙ{supTf(t) >b}. For each positive ε, we present Monte Carlo algorithms that run inconstanttime and compute the probabilities with relative error ε for arbitrarily largeb. 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.

scholarly journals Maxima of moving sums in a Poisson random field

2009 ◽  
Vol 41 (03) ◽  
pp. 647-663
Author(s):  
Hock Peng Chan
Keyword(s):  
Random Field ◽  
Random Fields ◽  
Gaussian Random Fields ◽  
Occupation Measure ◽  
Tail Probabilities ◽  
Alternative Representation ◽  
Asymptotic Formulae ◽  
Shape And Size ◽  
Asymptotic Tail

In this paper we examine the extremal tail probabilities of moving sums in a marked Poisson random field. These sums are computed by adding up the weighted occurrences of events lying within a scanning set of fixed shape and size. We also provide an alternative representation of the constants of the asymptotic formulae in terms of the occupation measure of the conditional local random field at zero, and extend these representations to the constants of asymptotic tail probabilities of Gaussian random fields.

scholarly journals Maxima of moving sums in a Poisson random field

2009 ◽  
Vol 41 (3) ◽  
pp. 647-663 ◽  
Author(s):  
Hock Peng Chan
Keyword(s):  
Random Field ◽  
Random Fields ◽  
Gaussian Random Fields ◽  
Occupation Measure ◽  
Tail Probabilities ◽  
Alternative Representation ◽  
Asymptotic Formulae ◽  
Shape And Size ◽  
Asymptotic Tail

In this paper we examine the extremal tail probabilities of moving sums in a marked Poisson random field. These sums are computed by adding up the weighted occurrences of events lying within a scanning set of fixed shape and size. We also provide an alternative representation of the constants of the asymptotic formulae in terms of the occupation measure of the conditional local random field at zero, and extend these representations to the constants of asymptotic tail probabilities of Gaussian random fields.

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