Random Measures

Abstract

A random measure may be thought of as a random set function which is almost surely a measure. Some results obtained by Ryll-Nardzewski for point processes on the real line are extended and the Laplace functional is introduced. Completely random measures, infinitely divisible random measures, and stationary random measures are characterized. Homogeneous random measures are introduced with examples and interpretations. A general characterization theorem for homogeneous random measures is proved. Finally, several applications of the theory of random measures are given.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1969
Accession Number
AD0856716

Entities

People

  • Michael G. Fahey

Organizations

  • Air Force Institute of Technology

Tags

Communities of Interest

  • Materials and Manufacturing Processes
  • Weapons Technologies

DTIC Thesaurus Topics

  • Air Force
  • Air Force Facilities
  • Engineering
  • Export Controls
  • Government (Foreign)
  • Mathematical Models
  • Mathematics
  • Models
  • North Carolina
  • Probability
  • Probability Distributions
  • Random Variables
  • Security
  • Stochastic Processes
  • Systems Analysis
  • Translations
  • United States

Readers

  • Mathematical Modeling and Probability Theory.