Study Of Generalized Poisson Process And Its Sum

Poisson process is very important in probability theory.Its actual background is thatthe number of customers arrive in service station. The application of generalizedPoisson process which derived from Poisson processes was widely concerned. So, thestudy on the property of generalized Poisson process has certain practical significance.This paper studied the sum of two independent generalized Poisson process.Theemphasis and innovation of this paper lied in deducing the generalized Poisson process{X (t), t≥0}characteristic function; giving the mean and the variance of the generalizedPoisson process;Proving that the sum of two independent generalized poisson processwas still a generalized Poisson process;and deriving its sum process characteristicfunction,mean and variance.This paper also received the conclusion that limitedindependent Poisson process sequence{X k(t), t≥0}(k=1,2…n)combinationis(?)is generalized Poisson process and solved the characteristicfunction,mean and variance of (?).