Large deviations of the \(L^p\)-norm of a Wiener process with drift
type: Item
instance of: scholarly article
title: Large deviations of the \(L^p\)-norm of a Wiener process with drift
zbMATH Open document ID: 0970.60025
DOI: 10.1007/BF02675079
author: V. R. Fatalov
published in: Mathematical Notes
publication date: 2001-10-06T00:00:00Z
review text: The aim of the present paper is to prove a large deviation result for some special shifts of the Wiener process \(W\) on \([0,1]\). More precisely, let \(2\leq p<\infty\) and \(0<c<(p+1)^{1/p}\), the author gives the exact asymptotic of \((\int_0^1|W(t)+ uct|^p dt>u^p)\) as \(u\to\infty\). The investigation of this question leads to a complicated boundary problem for a second-order differential operator and which may be reduced to the determination of the zeros of certain Legendre functions.
reviewed by: Werner Linde
Mathematics Subject Classification ID: 60F10
Mathematics Subject Classification ID: 60G15
zbMATH DE Number: 1470978
zbMATH Keywords: large deviation
zbMATH Keywords: Wiener process
zbMATH Keywords: Legendre functions
MaRDI profile type: Publication
cites work: Q3808953
cites work: Gaussian measure of large balls in \(l_ p^ 1\)
cites work: Q3362509
cites work: Q4375266
cites work: The Laplace method for probability measures in Banach spaces
cites work: Exact asymptotics of large deviations for Gaussian measures on Hilbert space
cites work: Q5519244
cites work: Q4481373
cites work: Q3689920
cites work: Gaussian measures on L\(_p\) spaces, \(1\leq p \leq \infty\)
cites work: Q5519417
cites work: Q3663911
cites work: Q4749793
description: scientific article; zbMATH DE number 1470978