On the distribution of supremum of diffusion local time
type: Item
instance of: scholarly article
title: On the distribution of supremum of diffusion local time
zbMATH Open document ID: 0796.60080
DOI: 10.1016/0167-7152(93)90220-D
published in: Statistics \& Probability Letters
publication date: 1994-09-20T00:00:00Z
review text: \((X(t), P_ x)_{t\geq 0}\) is a one-dimensional regular diffusion on an interval with transitions \(p(t,x,y)\) and local time \(L_{t,x}\). The law of \(\sup_{t\geq 0}(L_{t,x}-\mu t)\), \(\mu\geq 0\), is computed to be under \(P_ x\) an exponential distribution with parameter \(\alpha^*(x)/\mu\), where \(\alpha^*\) is the unique positive solution of \(\alpha/\mu-1/G_ \alpha=0\), where \(G_ \alpha\) is the Green kernel \(\int\exp(-\alpha t)p(t,x,y)=dt\).
reviewed by: Michael Kohlmann
Mathematics Subject Classification ID: 60J60
Mathematics Subject Classification ID: 60J55
zbMATH DE Number: 503673
zbMATH Keywords: local time
zbMATH Keywords: regular diffusion
zbMATH Keywords: exponential distribution
zbMATH Keywords: Green kernel
author: Paavo Salminen
MaRDI profile type: Publication
cites work: Fluctuation theory in continuous time
cites work: Q4772511
full work available at URL: 0167-7152(93)90220-d
OpenAlex ID: W1998271052
description: scientific article; zbMATH DE number 503673