Asymptotic expansions for renewal measures in the plane
type: Item
instance of: scholarly article
title: Asymptotic expansions for renewal measures in the plane
zbMATH Open document ID: 0638.60053
DOI: 10.1007/BF00348749
publication date: 1988-01-01T00:00:00Z
review text: Let P be a distribution in the plane and define the renewal measure \(R=\sum P^{*n}\) where * denotes convolution. The main results of this paper are three term asymptotic expansions for R far from the origin. As an application, expansions are obtained for distributions in linear boundary crossing problems.
Mathematics Subject Classification ID: 60F99
Mathematics Subject Classification ID: 60G50
Mathematics Subject Classification ID: 60K05
zbMATH DE Number: 4040962
zbMATH Keywords: renewal measure
zbMATH Keywords: convolution
zbMATH Keywords: boundary crossing problems
zbMATH Keywords: random walks
zbMATH Keywords: Fourier analysis
zbMATH Keywords: central limit theorem
author: Robert W. Keener
MaRDI profile type: Publication
cites work: Renewal Theory in the Plane
cites work: Remainder term estimates of the renewal function
cites work: Q5624436
cites work: Functions of discrete probability measures: Rates of convergence in the renewal theorem
cites work: On subordinated distributions and generalized renewal measures
cites work: Two theorems inr-dimensional renewal theory
cites work: Q5587584
cites work: Q5610807
cites work: On Moment Generating Functions and Renewal Theory
cites work: On Characteristic Functions and Renewal Theory
full work available at URL: https://doi.org/10.1007/bf00348749
OpenAlex ID: W2035924148
published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 4040962