Study Of Delayed Regenerative Phenomena And ε-Regenerative Phenomena

Delayed Regenerative Phenomena andε-Regenerative Phenomena are the development of Regenerative phenomena. In this dissertation, the probability background and property of three Regenerative Phenomena are summarized; in particular, the research findings in relation to the property of Delayed Regenerative Phenomena andε-Regenerative Phenomena.Kingman J.F.C. defined discrete Delayed Regenerative Phenomena and studied it. In order to study discrete Delayed Regenerative Phenomena, we study Delayed Renewal Sequence. Semi-group structure,Delphic property and denseness of Delayed Renewal Sequence are also presented in the dissertation.Secondly, we studyε-Regenerative Phenomena through p-a sequence. The semigroup property of p-a sequence has been proved, but the study of the power of p-a sequence has no progress. This dissertation works out a sufficient condition for the power of a a-sequence to be still a a-sequence, that is the closure of the power of a-sequence.At last, dissertation works out some new property of p-a sequence through studying Delayed Renewal Sequence and p-a sequence. The uniqueness,decomposability and Delphic property of p-a sequence are also prospected.