Joint distribution of the first hitting time and first hitting place for a random walk
type: Item
instance of: scholarly article
title: Joint distribution of the first hitting time and first hitting place for a random walk
zbMATH Open document ID: 0921.60066
author: Tadashi Nakajima
published in: Kodai Mathematical Journal
publication date: 1999-09-29T00:00:00Z
review text: \textit{W. Feller} [``An introduction to probability theory and its applications. Vol. II'' (1971; Zbl 0219.60003)] gave a general formula to calculate the Laplace-Fourier transform of a joint distribution of the first hitting time and the first hitting place of \((-\infty,0)\) for a general random walk on the real line starting from 0. The present paper obtains a representation of Laplace-Fourier transform of the joint distribution of the first hitting time and the first hitting place of the set \((-\infty,-a)\) \((a>0)\), which gives a relation to the above mentioned Feller's result, i.e. with the joint distribution of those of the set \((-\infty,0)\). The leading idea is the Wiener-Hopf's factorization theorem. The result is applied to a random walk example frequently occurring in queueing theory.
reviewed by: Neculai Curteanu
Mathematics Subject Classification ID: 60G50
Mathematics Subject Classification ID: 60K25
zbMATH DE Number: 1269768
zbMATH Keywords: random walk
zbMATH Keywords: queueing theory
zbMATH Keywords: joint distribution
zbMATH Keywords: first hitting time
zbMATH Keywords: first hitting place
zbMATH Keywords: Laplace-Fourier transform
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2996/kmj/1138043873
OpenAlex ID: W2017134384
cites work: Q5538132
cites work: Q5624436
cites work: Q4374858
cites work: A Combinatorial Lemma and Its Application to Probability Theory
cites work: On the joint distribution of the first hitting time and the first hitting place to the space-time wedge domain of a biharmonic pseudo process
DOI: 10.2996/KMJ/1138043873
description: scientific article; zbMATH DE number 1269768