Renewal Theory in Two Dimensions: Basic Results,

Abstract

In the paper a unified theory for studying renewal processes in two dimensions is developed. Bivariate probability generating functions and bivariate Laplace transforms are the basic tools used in generalizing the standard theory of univariate renewal processes. Two examples involving the use of independent and correlated exponential distributions are presented. These are used to illustrate the general theory and explicit expressions for the two dimensional renewal density, the two dimensional renewal function, the correlation between the marginal univariate renewal counting processes, and other related quantities are derived. (Author)

Document Details

Document Type
Technical Report
Publication Date
Feb 01, 1973
Accession Number
AD0757068

Entities

People

  • Jeffrey J. Hunter

Organizations

  • University of North Carolina at Chapel Hill

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Geometry
  • Mathematics
  • Probability
  • Standards
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

  • Approximation Theory.
  • Theoretical Analysis.