Asymptotic Behaviour in Symbolic Markov Chains

Many random processes depending upon time appear in fact in interval even if the standard modelisation reduces it to the mean. It is the case for daily temperature, daily value of stocks. They are known with minimum and maximum values, during a period of time. Thus, they can be considered as multivalued stochastic processes. In another paper (Noirhomme-Fraiture and Cuvelier 2007) we have introduced the so-called symbolic stochastic processes and more particularly the symbolic Markov chains. In that case, we suppose that the process has no memory of the past. In this paper, after reminding the basic notions for symbolic Markov chains, we will present some asymptotic behaviour for these processes.