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On the Asymptotic Behavior of Recurrent and "Almost Recurrent" Events


Lamperti, John Williams (1957) On the Asymptotic Behavior of Recurrent and "Almost Recurrent" Events. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/ZEZC-ZN21.


NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. In connection with a recurrent event E, random variables of interest include [...], the time since the last occurrence of E, [...], the total time during which E occurs, and [...], the time between occurrences. In this thesis theorems are given concerning the limiting distributions of these and other quantities as n [approaches infinity]. It is shown that the same distributions apply in certain cases where E is not a recurrent event; this suggests the concept of an "almost recurrent event" which is shown to have the same asymptotic behavior as an "associated" recurrent event. These results extend and correlate previous work of Feller, Dynkin, Spitzer, and Darling and Kac. Finally, an occupation time theorem is proved for processes whose states comprise two classes separated by the occurrence of a recurrent event.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:(Mathematics and Philosophy)
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Mathematics
Minor Option:Philosophy
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Unknown, Unknown
Thesis Committee:
  • Unknown, Unknown
Defense Date:1 January 1957
Record Number:CaltechETD:etd-07142004-143902
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:2881
Deposited By: Imported from ETD-db
Deposited On:16 Jul 2004
Last Modified:16 Aug 2023 21:43

Thesis Files

PDF (Lamperti_jw_1957.pdf) - Final Version
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