Homogeneous And Non-homogeneous Poisson Process In Finite Interval

Sun Rongheng in [1] describes in detail the homogeneous and non-homogeneous Poisson process and its application, as well as Poisson process, Poisson process filtering, but these models are based on the[0, +∞). And in real life many cases, the Poisson flow may only a finite interval [a, b] in there, so the research of homogeneous and non-homogeneous Poisson process in finite interval has a theoretical value and practical significance.This article has been given the limited range [a, b] on the homogeneous and non-homogeneous Poisson process on the basis of the mathematical model, more in-depth study their statistical properties, given their mean function, variance Function, correlation function, covariance function and the characteristic function and study their distribution, given the time they reach the interval with the arrival distribution.This article in the adoption order a = 0,b= +∞, obtained finite interval [a, b] on the (non) homogeneous Poisson process is the Promotion of the (non) homogeneous Poisson process of promotion in [0, +∞). Re-use orderλ(t )=λ,obtained (?)Then obtain that a limited range of homogeneous Poisson process is a limited range of the non-homogeneous Poisson process specific situation. This result correspond that the homogeneous Poisson process of promotion in [0, +∞)is the non-homogeneous Poisson process special circumstances. This result on the one hand shows the conclusions of this paper is the Promotion of the Poisson process in [0, +∞), On the other hand also to a certain extent, verify the correctness of the conclusion.