Abstract
We consider a continuous-time Markov additive process (J
t
,S
t
) with (J
t
) an irreducible Markov chain on E = {1,…,s}; it is known that (S
t
/t) satisfies the large deviations principle as t → ∞. In this paper we present a variational formula H for the rate function κ∗ and, in some sense, we have a composition of two large deviations principles. Moreover, under suitable hypotheses, we can consider two other continuous-time Markov additive processes derived from (J
t
,S
t
): the averaged parameters model (J
t
,S
t
(A)) and the fluid model (J
t
,S
t
(F)). Then some results of convergence are presented and the variational formula H can be employed to show that, in some sense, the convergences for (J
t
,S
t
(A)) and (J
t
,S
t
(F)) are faster than the corresponding convergences for (J
t
,S
t
).
Publisher
Cambridge University Press (CUP)
Subject
Statistics, Probability and Uncertainty,General Mathematics,Statistics and Probability
Cited by
4 articles.
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