On the Asymptotic Behavior of Regenerative Processes and Functionals of Regenerative Processes.

Abstract

The asymptotic behavior of regenerative stochastic processes is considered. For the set (V sub 0(t), t > or = 0), a regenerative process, the author defines a strictly stationary regenerative process the set (V sub star(t), -infinity < t < infinity) which corresponds to the steady-state behavior of the set (V sub 0(t), t > or = 0) under very general conditions. The author proves, under very mild restrictions, that (V sub 0)(t) approaches (V sub star)(0) as t approaches infinity, correcting an error of Feller (An Introduction to Probability Theory and Its Applications, Vol. II, John Wiley and Sons, N.Y., 1966, p. 365). The remainder of the paper is devoted to the generalization of various asymptotic properties of regenerative processes to processes which are path-functionals of regenerative processes. (Author)

Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1971
Accession Number
AD0731069

Entities

People

  • Douglas R. Miller

Organizations

  • Cornell University

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Mathematics
  • Probability
  • Steady State
  • Stochastic Processes

Readers

  • Mathematical Modeling and Probability Theory.
  • Military History