Construction of Ito's excursion theory on birth and death processes

This paper combines birth and death processes with Ito's excursion theory,and builds it's frame structure under Ito's excursion which mainly includes local time,inverse local time,excursion,excursion space,excursion measure.It shows that {Yt,t∈DY} is a poisson point processe,and birth and death processes have Markov property under P(·).The excursion theory for birth and death processes is established.