Applications Of Algebraric Probability Theory In The Theory Of Regenerative Phenomena

Algerbriac Probability Theory is about the Arithemetic theory of Semigroup in the Probability theory ,for example ,Structure question,Decomposition question,Classification question,The Representation of Decompasable elements question,Anti-Prime elements and Prime elements's Representation question and so on .Delphic Semigroup,MD Semigroup,HD Semigroup,ZH Semigroup ,GZH Semigroup,Hun Semigroup and Hungarian Semigroup are powerful tools in researching Algerbriac Probability Theory.We study Delphic properties of a special semigroup (for example Positve Renewal Sequences ,Standard p-functions Semigroup and so on),Usually We try to prove that one of the semigroups above ,Then we use it to study the Delphic properties.In this paper,We study the Generalized delayed renewal sequences and semi-p-function arise from Renewal sequence and p-function in the theory of Regenerative Phenomena. Firstly ,The backgroud of Algerbriac Probability Theory , Delphic Semigroup and Extensions are summaried ,introduce the history and Extensions of the Renewal sequence and p-function. Secondly ,on the third chapt , we discussed the relations among the Generalised Delayed Renewal Sequences, Delayed Renewal Sequences and Positive Delayed Renewal Sequences,and proved Some Foundamental Properties Of Generalised Delayed Renewal Sequences,Give some countexample to illustrate.Finally ,On the fouth chapt ,Using Delphic Semigroup and Hun Semigroup to study the Algebraric-topologic proterties of the bounded Semi-p-function semeigroup and Proved some fountmental propertie in the Hun Semigroup.