Abstract
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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Athreya, F. and P. Ney (1978). Limit theorems for semi-Markov processes. Bull.Austral.Math.Soc. 19, 283–294.
Iscoe, I., P. Ney and E. Nummelin (1984). Large deviations of uniformly recurrent Markov additive processes. Adv. in Appl. Math. To appear.
Ney, P. and E. Nummelin (1984). Markov additive processes I: Eigenvalue properties and limit theorems. University of Wisconsin technical report.
Ney, P. and E. Nummelin. (1985). Markov additive processes II: Large deviations. Univ.of Wisconsin. Report.
Niemi, S. and E. Nummelin (1984). On nonsingular renewal kernels with an application to a semigroup of transition kernels. University of Helsinki technical report.
Nummelin, E. (1978). Uniform and ratio limit theorems for Markov renewal and semi-regenerative processes on a general state space. Ann.de l’Inst.H.Poincaré, B 14, 119–143.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1986 Springer Science+Business Media New York
About this chapter
Cite this chapter
Ney, P., Nummelin, E. (1986). Some limit theorems for Markov additive processes. In: Janssen, J. (eds) Semi-Markov Models. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-0574-1_1
Download citation
DOI: https://doi.org/10.1007/978-1-4899-0574-1_1
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4899-0576-5
Online ISBN: 978-1-4899-0574-1
eBook Packages: Springer Book Archive