具有反射壁的随机环境中单生链的灭绝概率计算

Torrez(1979)借助于矩阵求出了两边界均为吸收壁的随机环境中生灭链的灭绝概率。借鉴此方法，研究了状态空间为{0,1,…，M}具有反射壁的随机环境中单生链的灭绝概率，得到了关于灭绝概率的差分方程。随机环境中生灭链作为随机环境中单生链的特例，相应的结果也在文中得到，并应用到具体的例子。具体而言，有如下主要结论：1）求出了0为吸收壁的马氏环境中单生链的灭绝概率；2）求出了0为吸收壁，M为反射壁的马氏环境中单生链的灭绝概率；3）求出0为吸收壁，M为反射壁的马氏环境中生灭链的灭绝概率；4）求出了0为吸收壁，M为反射壁的马氏环境中齐次生灭链的灭绝概率。

Calculating Extinction Probabilities for the Single Birth Chain with a Reflecting Barrier in a Random Environment

Torrez(1979) calculated the extinction probabilities for the birth and death chain in a random environment with its both boundary points as absoption barriers.Using the method appearing,author calculates the extinction probabilities for the single birth chain in a random environment with a reflecting barrier and with { 0,1,...,M } as its state space,and obtains the vector difference equations about them.Extinction probabilities for the birth and death chain in a random environment--a special case of the single birth chain in a random environment are also obtained and the results are applied into examples.The main results are calculated as the following: 1) Extinction probabilities for the single birth chain in Markovian environment with the absorption barrier 0. 2) Extinction probabilities for the single birth chain in Markovian environment with the absorption barrier 0 and the reflecting barrier M . 3) Extinction probabilities for the birth and death chain in Markovian environment with the absorption barrier 0 and the reflecting barrier M . 4) Extinction probabilities for the homogeneous birth and death chain in Markovian environment with the absorption barrier 0 and the reflecting barrier M .