Skip-free 馬可夫鏈的遞移機率

Abstract

對具有某些條件的 skip-free 馬可夫鏈, 只要利用其 infinitesimal matrix 的特徵值, 即可得到其遞移機率的正確形式. Consider an ergodic continuous time Markov chain X(t) with an infinitesimal matrix Q defined on a finite state space and the eigenvalues of Q are distinct. In this article, we prove that if X(t) is skip-free, then the transition probability can be exactly found in an alernative way rather than using Kolmogo- rov's Backward equations.