非突变有限生灭系统的瞬态解

The Transient Solution for Non-mutation Finite Birth-Death Process

研究了非突变有限生灭系统,利用系统转移速率矩阵的特殊形式,以Caley-Hamilton定理为基础,结合齐次线性递归系统的通解,获得了该系统形式简洁,计算比较封闭的幂级数形式的瞬态解,并给出了系数的确定方法,最后通过数值仿真验证了解的可靠性.

The non-mutation finite birth-death process is studied.A simple transient solution is obtained for the power series form of the system based on Caley-Hamilton theorem by using the special form of transient rate matrix,and the coefficient in the power series satisfies the homogeneous linear recurrence relations,which enables fast and accurate numerical computations.The reliability for transient probability function has been illustrated by a numerical example in the end.