经2状态马氏修正的Poisson过程的极大似然估计

A Maximum Likelihood Estimation for Two States Markov-Modulated Poisson Processes

近年来,隐马氏模型成为研究相依随机变量的一个十分有用的工具。应用过程中的一个很重要的问题是如何对隐马氏模型的参数进行估计。一般使用的方法是将连续时间隐马氏模型的问题转化为离散时间隐马氏模型的问题来讨论,本文用此方法讨论一类连续时间隐马氏模型——状态个数为2的经马氏链修正的Poisson过程的极大似然估计及其算法。此类模型被广泛用来对复杂通信网络的通信流进行建模。

During the last decade, Hidden Markov models(HMMs) have become a widespread tool for modeling sequence of dependent variables. The most important problem in application is how to (estimate) the parameter of the HMMs. By changing continued-time HMMs into discrete-time HMMs is the commom way to deal with it. In this paper, using the similar method we consider maximum (likelihood) estimation for one kind of special HMMs, which is called Markov-modulated Poisson (processes) was given when its state number is 2. Such processes have been proposed for modeling (traffic) streams in complex telecommunication networks.