On some stochastic models for replication of character strings

In this note, some probabilistic models for replication of character strings are considered. These replication processes involve random mutations, deletions and insertions of characters. We investigate invariance of certain probabilistic properties of replicating character strings under the proposed stochastic models for the replication process. It is shown that some well-known types of hidden Markov models with finite state spaces arise as special cases of our stochastic replication models. We also introduce the notion of a hidden mixed Markov model for a character string that arises in a situation where the replication process satisfies exchangeability conditions.