Sharp asymptotics of large deviations for general state-space Markov-additive chains in Rd

For {xi(i)} subset of R-d, i = 0, 1, 2, .... Markov-additive (MA) random variables, d greater than or equal to 2, S-n = Sigma(i)(= 0)(n) xi(i), and (X-n, S-n) a phi-irreducible, aperiodic, time-homogeneous MA-chain, a = inf(x epsilon) r I(x), we extend to general state-space chains, under a regeneration hypothesis, asymptotic results of the form P(S-n epsilon n Gamma;X-n epsilon A) = n(V)e(-na)(d(0) + o(l)) as n --> infinity. (C) 2000 Elsevier Science B.V. All rights reserved.