Large deviations of the \(L^p\)-norm of a Wiener process with drift
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.
scientific article; zbMATH DE number 1470978
scientific article