On the homogeneous birth-and-death process and its integral
齐次生灭过程及其积分
In a simple homogencous birth-and-death process with λ and μ as the constant birth and death rates, tespectively, let Xt denote the population size at time t and Y(t) = ∮t0X(u) du. The results obtained include among others the following: (i) An emplicit formula for the characteristic function of the joint distribution of X(t) and Yt). (ii) It is shown that, if t↑∞ while λ ≤ μ, jkthe limitaing distribution of Y(t) is aweighted mean of certain X2-distributions. If λ > μ, then…