Stationary and Transition Probabilities in Slow Mixing, Long Memory Markov Processes

摘要

We observe a length- (n) sample generated by an unknown, stationary ergodic Markov process (model) over a finite alphabet ( {cal A}) . Given any string ( {mathbf{w}}) of symbols from ( {cal A}) we want estimates of the conditional probability distribution of symbols following ( {mathbf{w}}) , as well as the stationary probability of ( {mathbf{w}}) . Two distinct problems that complicate estimation in this setting are: 1) long memory and 2) slow mixing, which could happen even with only one bit of memory.