Discrete time uniformly recurrent Markov additive processes: two simplified models and large deviations
Pages: 51- 62
Received: 1 July 2003 Revised: 23 September 2003
Mathematics Subject Classification (2000): 60F10
Work partially supported by Murst Project "Processi Stocastici, Calcolo Stocastico e Applicazioni a Filtraggio, Controllo, Simulazione e Finanza Matematica
Abstract: In this paper we consider a discrete time uniformly recurrent Markov additive process ((Jn,Sn)) according to the presentation in . As in  (which deals with continuous time Markov additive processes with finite state space environment) we define the fluid model and the averaged parameters model as two simplified Markov additive processes derived from ((Jn,Sn)) in a suitable way. In this paper we prove some inequalities between rate functions which coincide with the analogous inequalities in .