Some limit theorems for Markov additive processes

  • Peter Ney
  • Esa Nummelin

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.

Keywords

Limit Theorem Slight Extension General State Space Countable Space Regeneration Construction 
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References

  1. Athreya, F. and P. Ney (1978). Limit theorems for semi-Markov processes. Bull.Austral.Math.Soc. 19, 283–294.MathSciNetMATHCrossRefGoogle Scholar
  2. Iscoe, I., P. Ney and E. Nummelin (1984). Large deviations of uniformly recurrent Markov additive processes. Adv. in Appl. Math. To appear.Google Scholar
  3. Ney, P. and E. Nummelin (1984). Markov additive processes I: Eigenvalue properties and limit theorems. University of Wisconsin technical report.Google Scholar
  4. Ney, P. and E. Nummelin. (1985). Markov additive processes II: Large deviations. Univ.of Wisconsin. Report.Google Scholar
  5. 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
  6. 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.MathSciNetMATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1986

Authors and Affiliations

  • Peter Ney
    • 1
  • Esa Nummelin
    • 2
  1. 1.Mathematics DepartmentUniversity of WisconsinWisconsinUSA
  2. 2.Department of MathematicsUniversity of HelsinkiFinland

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