NONPARAMETRIC ESTIMATION FOR A COMPOUND POISSON PROCESS GOVERNED BY A MARKOV CHAIN

摘要

The problem of nonparametric estimation for a Poisson process governed by a Markov chain with continuous time is considered in the case of incomplete observations. A method of the nonparametric estimation is proposed. The method is based on a representation of such a process in the form of a hidden Markov model.An example for the estimation of unknown distribution functions is considered in the case of incomplete observations after a compound Poisson process governed by a simple Markov regenerative process.