Statistical aspects of lumpability hypotheses for Markov chains

Abstract

Under certain conditions the state space of a discrete parameter Markov Chain may be partitioned to form a smaller lumped chain that retains the Markov property. The problem of formulating lumpability hypotheses when the transition probability matrix P is not known and, hence, must be estimated is discussed. An approximate test of these hypotheses is described based on well known non-parametric methods. The procedure is illustrated by an example. (Author)