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Type of Document	Dissertation
Author	Lamperti, John
URN	etd-07142004-143902
Persistent URL	http://resolver.caltech.edu/CaltechETD:etd-07142004-143902
Title	On the asymptotic behavior of recurrent and "almost recurrent" events
Degree	PhD
Option	Mathematics
Advisory Committee	Advisor Name Title Unknown Committee Member
Keywords	none
Date of Defense	1957-01-01
Availability	unrestricted
Abstract 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.
Files	Filename       Size       Approximate Download Time (Hours:Minutes:Seconds)     28.8 Modem   56K Modem   ISDN (64 Kb)   ISDN (128 Kb)   Higher-speed Access    Lamperti_jw_1957.pdf 1.66 Mb 00:07:41 00:03:57 00:03:27 00:01:43 00:00:08