In this article, we consider sequences of partial sums of iid Gaussian random sets (with respect to the Minkowski sum) and we study the asymptotic behavior of some hitting probabilities (of suitable sets of (Formula presented.)) for these partial sums. We also illustrate the use of the importance sampling for the estimation of these hitting probabilities by Monte Carlo simulations. We obtain the analog of well-known results for level crossing probabilities of random walks, and we refer to a version of the classical Cramér's Theorem in large deviations for random compact sets existing in the literature.

Macci, C., Pacchiarotti, B. (2017). Asymptotic behavior of some hitting probabilities for sums of IID gaussian random sets. COMMUNICATIONS IN STATISTICS. SIMULATION AND COMPUTATION, 46(6), 4318-4332 [10.1080/03610918.2015.1116569].

Asymptotic behavior of some hitting probabilities for sums of IID gaussian random sets

MACCI, CLAUDIO;PACCHIAROTTI, BARBARA
2017

Abstract

In this article, we consider sequences of partial sums of iid Gaussian random sets (with respect to the Minkowski sum) and we study the asymptotic behavior of some hitting probabilities (of suitable sets of (Formula presented.)) for these partial sums. We also illustrate the use of the importance sampling for the estimation of these hitting probabilities by Monte Carlo simulations. We obtain the analog of well-known results for level crossing probabilities of random walks, and we refer to a version of the classical Cramér's Theorem in large deviations for random compact sets existing in the literature.
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/06 - Probabilita' e Statistica Matematica
English
Importance sampling; Large deviations; Minkowski sum; Statistics and Probability; Modeling and Simulation
http://www.tandf.co.uk/journals/titles/03610918.asp
Macci, C., Pacchiarotti, B. (2017). Asymptotic behavior of some hitting probabilities for sums of IID gaussian random sets. COMMUNICATIONS IN STATISTICS. SIMULATION AND COMPUTATION, 46(6), 4318-4332 [10.1080/03610918.2015.1116569].
Macci, C; Pacchiarotti, B
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/183852
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