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