The moments of the area under reflected Brownian bridge conditional on its local time at zero
type: Item
instance of: scholarly article
title: The moments of the area under reflected Brownian bridge conditional on its local time at zero
zbMATH Open document ID: 0965.60081
DOI: 10.1155/S1048953300000137
author: Frank B. Knight
published in: Journal of Applied Mathematics and Stochastic Analysis
publication date: 2001-08-05T00:00:00Z
full work available at URL: https://eudml.org/doc/48834
review text: Let \(U_T\) denote the real Brownian bridge of duration \(T\), and \(\ell(x)= L^x_T(|U_T|)\) the total local time at \(x\) of its absolute value. A recursion formula for the conditional moments of \(\int^T_0|U_T(s) |ds\) given \(\ell(0)\) is developed. The method is based on the Kac formula relative to the process \((\ell(x), 1-\int^x_0 \ell(u)du)\) recently introduced by Pitman, and on power series expansions. An integral expression for the joint moments of the areas of the positive and negative parts of the Brownian bridge \(U_T\) is deduced.
reviewed by: Jacques Franchi
Mathematics Subject Classification ID: 60J65
Mathematics Subject Classification ID: 60J60
zbMATH DE Number: 1507624
zbMATH Keywords: Brownian bridge
zbMATH Keywords: local time
zbMATH Keywords: Kac formula
zbMATH Keywords: Pitman process
zbMATH Keywords: Hermite equations
MaRDI profile type: Publication
OpenAlex ID: W2150831438
description: scientific article; zbMATH DE number 1507624