Equivalence of hidden Markov models

Abstract The hidden Markov information source (process) is a stochastic process with a finite‐state Markov chain behind it, and the state cannot directly be observed, while only a function of the state is observed as a stream of symbols. This kind of process is very important in both theory and application, but its theoretical structure has not been clarified. This paper gives a sufficient condition for two hidden Markov processes based on different Markov chains to be equivalent as the stochastic process. The condition for that condition to be necessary also is shown. A condition for a hidden Markov process to be equivalent to a Markov chain also is presented.