关于马氏过程散度的极限性质

在有限状态空间中取值的随机变量序列,假设它在概率测度P下是一非齐次马氏链,在概率测度Q下是一齐次马氏链,利用非齐次马氏信源的渐近均分割性,齐次马氏信源的渐近均分割性及随机变量序列的一致可积性,给出了马氏过程散度的极限存在条件,并得到了马氏过程散度的极限的值,在此基础上将马氏过程散度的极限存在条件推广到了高阶马氏过程的情形,同时也给出了高阶马氏过程散度的极限的值.

Limit properties for divergence of Markov processes

A sequence of random variables take values in the finite alphabet set,assuming a nonhomogeneous Markov chains under a probability measure P and a homogeneous Markov chains under a probability measure Q.The AEP for Markov information and the uniform integrability of random variable sequences are applied to give the limit properties for the divergence of Markov processes and the limit is computed.An extension of the conclusion for the case of m order Markov chains is given.