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On non-singular renewal kernels with an application to a semigroup of transition kernels

Author

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  • Niemi, S.
  • Nummelin, E.

Abstract

We study the non-singularity and limit properties of the renewal kernel R=[summation operator]K*n associated with a positive convolution kernel K(x,dyxdt) defined on a general measurable space (E, ). The principal tool is the use of embedded renewal measures. As an application we consider continuous parameter semigroups (Rt(x,dy);t[greater-or-equal, slanted]0) of transition kernels on (E, ).

Suggested Citation

  • Niemi, S. & Nummelin, E., 1986. "On non-singular renewal kernels with an application to a semigroup of transition kernels," Stochastic Processes and their Applications, Elsevier, vol. 22(2), pages 177-202, July.
    • Handle: RePEc:eee:spapps:v:22:y:1986:i:2:p:177-202
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    Cited by:

    1. Kyprianou, Andreas E. & Palau, Sandra, 2018. "Extinction properties of multi-type continuous-state branching processes," Stochastic Processes and their Applications, Elsevier, vol. 128(10), pages 3466-3489.
    2. Gerold Alsmeyer, 2003. "On the Harris Recurrence of Iterated Random Lipschitz Functions and Related Convergence Rate Results," Journal of Theoretical Probability, Springer, vol. 16(1), pages 217-247, January.
    3. Alsmeyer, Gerold & Hoefs, Volker, 2002. "Markov renewal theory for stationary (m+1)-block factors: convergence rate results," Stochastic Processes and their Applications, Elsevier, vol. 98(1), pages 77-112, March.

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