Some limit theorems for Markov additive processes
At the Semi-Markov Symposium we presented some new results on Markov-additive processes which will be published in Ney and Nummelin (1984), Ney and Nummelin (1985). In their proofs we used regeneration constructions similar to those in several previous papers (Athreya and Ney, 1978; Nummelin, 1978; Iscoe, Ney and Nummelin, 1984). The proof of the particular regeneration used in Ney and Nummelin (1984) was omitted, and we will now provide it here. We also prove a slight extension of the results in Iscoe, Ney and Nummelin (1984); Ney and Nummelin (1984), and summarize the results we announced at the symposium.
KeywordsLimit Theorem Slight Extension General State Space Countable Space Regeneration Construction
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- Iscoe, I., P. Ney and E. Nummelin (1984). Large deviations of uniformly recurrent Markov additive processes. Adv. in Appl. Math. To appear.Google Scholar
- Ney, P. and E. Nummelin (1984). Markov additive processes I: Eigenvalue properties and limit theorems. University of Wisconsin technical report.Google Scholar
- Ney, P. and E. Nummelin. (1985). Markov additive processes II: Large deviations. Univ.of Wisconsin. Report.Google Scholar
- Niemi, S. and E. Nummelin (1984). On nonsingular renewal kernels with an application to a semigroup of transition kernels. University of Helsinki technical report.Google Scholar