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The Dynamic Behaviour of Non-Homogeneous Single-Unireducible Markov and Semi-Markov Chains

In: Networks, Topology and Dynamics

Author

Listed:
  • Guglielmo D'Amico

    (Dipartimento di Scienze del Farmaco Università “G.D'Annunzio”)

  • Jacques Janssen

    (Jacan EURIA & Université de Bretagne Occidentale)

  • Raimondo Manca

    (Finanziarie ed Assicurative Università di Roma “La Sapienza”)

Abstract

In this paper single-unireducible Markov and semi-Markov chains are defined and their dynamic behaviour is analysed. The main results concern the asymptotic study of these processes. In fact it is proved that the topological structure of single-unireducibility represents a sufficient condition that guarantees the absorption after a sufficiently long period in the absorbing class for both Markov and semi-Markov chains. The probabilistic results are based on graph theory using relations between the graphs and transition matrices.

Suggested Citation

  • Guglielmo D'Amico & Jacques Janssen & Raimondo Manca, 2009. "The Dynamic Behaviour of Non-Homogeneous Single-Unireducible Markov and Semi-Markov Chains," Lecture Notes in Economics and Mathematical Systems, in: Ahmad K. Naimzada & Silvana Stefani & Anna Torriero (ed.), Networks, Topology and Dynamics, pages 195-211, Springer.
    • Handle: RePEc:spr:lnechp:978-3-540-68409-1_10
    DOI: 10.1007/978-3-540-68409-1_10
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    Cited by:

    1. Guglielmo D’Amico & Jacques Janssen & Raimondo Manca, 2010. "Initial and Final Backward and Forward Discrete Time Non-homogeneous Semi-Markov Credit Risk Models," Methodology and Computing in Applied Probability, Springer, vol. 12(2), pages 215-225, June.

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