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

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 ) 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.

KEYWORDS:

• Importance sampling
• Large deviations
• Minkowski sum

MATHEMATICS SUBJECT CLASSIFICATION:

• 60D05
• 60F10
• 65C05

Acknowledgments

We thank the referee for the careful reading of the article. The comments led to an improvement of the presentation of the article. The support of GNAMPA (INDAM) is acknowledged.