High Extremes of Gaussian Chaos Processes: A Discrete Time Approximation Approachстатья
Информация о цитировании статьи получена из
Web of Science,
Scopus
Статья опубликована в журнале из списка Web of Science и/или Scopus
Дата последнего поиска статьи во внешних источниках: 21 мая 2019 г.
Аннотация:Let $\mathbf{\boldsymbol{\xi}}(t)=(\xi_{1}(t),\ldots,\xi_{d}(t))$ be a Gaussian zero mean stationary a.s. continuous vector process. Let $g\colon{\mathbb{R}}^{d}\to {\mathbb{R}}$ be a homogeneous function of positive degree. We study probabilities of high extrema of the Gaussian chaos process $g(\mathbf{\boldsymbol{\xi}}(t))$. Important examples are products of Gaussian processes, $\prod_{i=1}^{d}\xi_{i}(t)$, and quadratic forms $\sum_{i,j=1}^{d}a_{ij}\xi_{i}(t)\xi_{j}(t)$. Methods of our studies include the Laplace saddle point asymptotic approximation and the double sum asymptotic method for probabilities of high excursions of Gaussian processes. For the first time, using the double sum method, we apply the discrete time approximation with refining grid.