Massive excursions of Gaussian isotropic fields. Method of momentsстатья
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Дата последнего поиска статьи во внешних источниках: 6 декабря 2018 г.
Аннотация:The asymptotic behavior of probability of large massive excursions above a high
level is evaluated for Gaussian isotropic twice differentiable Gaussian fields. A massive excursion is
the excursion with base diameter exceeding a fixed positive number. For proofs, we introduce and
study a vector Gaussian process with components that are independent copies of the initial field,
and consider the point process of exits of trajectories of this process from an appropriate infinitely
expanding set. By studying the asymptotic behavior of the first and second moments of distribution
of this point process, the desired asymptotic behavior is obtained. Moreover, general results on the
logarithmic (rough) asymptotic behavior of the large massive excursion probabilities are put forward.