Sojourn times
type: Item
instance of: scholarly article
title: Sojourn times
zbMATH Open document ID: 0867.60026
DOI: 10.1155/S1048953396000366
author: Lajos Takács
published in: Journal of Applied Mathematics and Stochastic Analysis
publication date: 1997-07-20T00:00:00Z
full work available at URL: https://eudml.org/doc/47672
review text: Summary: Let \(\{\zeta(u), u\geq 0\}\) be a stochastic process with state space \(A\cup B\) where \(A\) and \(B\) are disjoint sets. Denote by \(\beta(t)\) the total time spent in state \(B\) in the interval \((0,t)\). This paper deals with the problem of finding the distribution of \(\beta(t)\) and the asymptotic distribution of \(\beta(t)\) as \(t\to\infty\) for various types of stochastic processes. The main result is a combinatorial theorem which makes it possible to find in an elementary way, the distribution of \(\beta(t)\) for homogeneous stochastic processes with independent increments.
Mathematics Subject Classification ID: 60G50
Mathematics Subject Classification ID: 60J55
zbMATH DE Number: 988080
zbMATH Keywords: stochastic processes
zbMATH Keywords: sojourn times
zbMATH Keywords: distributions
zbMATH Keywords: limit distributions
MaRDI profile type: Publication
OpenAlex ID: W4240607324
description: scientific article; zbMATH DE number 988080