Study Of Regenerative Phenomena Semi-group

Algebraic Probability Theory is about the algebraic-topologic property of semigroup in the probability model(arithematic theory),for example decomposition theory and central limit property.The probability background of the three Regenerative Phenomena and the properties of Regenerative Phenomena.In particular,the results of the Delayed Regenerative Phenomena andε- Regenerative Phenomena.Firstly,For discret Delayed Regenerative Phenomena,we study delayed renewal sequences.The result of power of renewal sequences be also renewal sequences is proved.But the power of renewal sequences isn't proved yet at present. This paper works out a sufficient condition for the power of a delay renewal sequence to be still a delay renewal sequence and generalize to result to the power of generalized delay renewal sequences.Secondly,We use p-a pairs to realize to studyε- Regenerative Phenomena.We recognize some decomposible p-a pairs. The problem of unique p-a pairs is also discuss in this paper, three criteria are obtained .Thirdly,we show the semigroup of p-functions defined on a semigroup is a stable Hun semigroup. It will become a Delphic semigroup we give some property to the semigroup on which the p-function is defined.