Accession Number : AD0731069

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

Descriptive Note : Technical rept.,

Corporate Author : CORNELL UNIV ITHACA N Y DEPT OF OPERATIONS RESEARCH

Personal Author(s) : Miller,Douglas R.

Report Date : AUG 1971

Pagination or Media Count : 77

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)

Descriptors :   (*STOCHASTIC PROCESSES, ASYMPTOTIC SERIES), DISTRIBUTION FUNCTIONS, CONVERGENCE, RANDOM VARIABLES, INTEGRALS, INEQUALITIES, THEOREMS, THESES

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE