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Some limit theorems for Markov additive processes

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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.

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References

  • Athreya, F. and P. Ney (1978). Limit theorems for semi-Markov processes. Bull.Austral.Math.Soc. 19, 283–294.

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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.

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  • Ney, P. and E. Nummelin (1984). Markov additive processes I: Eigenvalue properties and limit theorems. University of Wisconsin technical report.

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  • Ney, P. and E. Nummelin. (1985). Markov additive processes II: Large deviations. Univ.of Wisconsin. Report.

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  • Niemi, S. and E. Nummelin (1984). On nonsingular renewal kernels with an application to a semigroup of transition kernels. University of Helsinki technical report.

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  • 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.

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Author information

Authors and Affiliations

  1. Mathematics Department, University of Wisconsin, Wisconsin, 53706, USA

    Peter Ney

  2. Department of Mathematics, University of Helsinki, Finland

    Esa Nummelin

Authors
  1. Peter Ney
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  2. Esa Nummelin
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Editor information

Editors and Affiliations

  1. Free University of Brussels, Brussels, Belgium

    Jacques Janssen

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© 1986 Springer Science+Business Media New York

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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

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  • 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

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