Density of the probability of a large rejection of a Gaussian stochastic process. II
type: Item
instance of: scholarly article
title: Density of the probability of a large rejection of a Gaussian stochastic process. II
zbMATH Open document ID: 0675.60030
DOI: 10.1007/BF00966264
author: S. H. Smith
published in: Lithuanian Mathematical Journal
publication date: 1987-01-01T00:00:00Z
review text: [For part I, see Litov. Math. Sb. 26, No.3, 512-529 (1986; Zbl 0634.60036)]. Let \(\xi\) (t), \(t\in R^ 1\), be a differentiable Gaussian process, E \(\xi\) (t)\(=0\), Var \(\xi\) (t)\(=Var \xi '(t)=1\). Asymptotic properties of the probability \[ P(y)=P(-y_ 1(t)<\xi (t)<y_ 2(t),\quad t\in [0,T]\} \] and its derivatives \(P'(y,\mu)=\lim_{h\to 0}[P(y+h\mu)-P(y)]/h\) are considered when \(y_ i(t)\to \infty\), \(i=1,2\) and \(T\to \infty\).
Mathematics Subject Classification ID: 60G15
Mathematics Subject Classification ID: 60G10
Mathematics Subject Classification ID: 60F10
zbMATH DE Number: 4105961
zbMATH Keywords: density
zbMATH Keywords: runaway
zbMATH Keywords: Gaussian process
zbMATH Keywords: Asymptotic properties
MaRDI profile type: Publication
cites work: Q3772991
cites work: Probability of a large rejection of a nonstationary Gaussian process. II
description: scientific article; zbMATH DE number 4105961