On the Asymptotic Behavior of Regenerative Processes and Functionals of Regenerative Processes.
CORNELL UNIV ITHACA N Y DEPT OF OPERATIONS RESEARCH
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The asymptotic behavior of regenerative stochastic processes is considered. For the set V sub 0t, t or 0, a regenerative process, the author defines a strictly stationary regenerative process the set V sub start, -infinity t infinity which corresponds to the steady-state behavior of the set V sub 0t, t or 0 under very general conditions. The author proves, under very mild restrictions, that V sub 0t approaches V sub star0 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
- Statistics and Probability