Optimal local first exit time
type: Item
instance of: scholarly article
title: Optimal local first exit time
zbMATH Open document ID: 1218.60032
author: S. S. Rasova
author: B. P. Harlamov
published in: Journal of Mathematical Sciences (New York)
publication date: 2009-11-13T00:00:00Z
review text: The authors study the properties of local first exit times from an interval \((-\infty, b)\) in the line by a generic class of processes on the real line. They relate such times to upcrossing times of the process of intervals of the type \((b-r, b)\), and show how to compute the expected value of a class of functionals that appear naturally in the theory of system reliability. Typical functionals are of the type \[ C -v E_x[\int_0^\tau\exp(-\int_0^t(X_s)\,ds)\,dt]-wE_x[\exp(-\int_0^\tau(X_s)\,ds)]. \] The problem of studying the nature of the local first exit time is the first step toward the computation of these functionals. Then comes the problem of determining the properties of the minimizing \(\tau\). They do this in some particular cases.
reviewed by: Henryk Gzyl
Mathematics Subject Classification ID: 60G40
zbMATH DE Number: 5632984
MaRDI profile type: Publication
full work available at URL: s10958-009-9445-8
OpenAlex ID: W2001196644
cites work: Exact solutions and transformations of heat and wave theory equations.
cites work: Continuous Semi‐Markov Processes
cites work: Q5695308
cites work: Q4251683
DOI: 10.1007/S10958-009-9445-8
description: scientific article; zbMATH DE number 5632984