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Limiting distributions of time averages of additive functionals defined on a semi-Markov process

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We consider an additive functional ζton a continuous time semi-Markov process with an arbitrary state space. We study the existence of the limiting distribution of ζt/t without the condition of the finiteness of the mean occupation time of a fixed state.

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Literature cited

  1. V. M. Shurenkov, “Asymptotics of potentials of a terminating ergodic Markov chain,” in: Some Problems in the Theory of Stochastic Processes, Kiev Institute of Mathematics, Academy of Sciences of Ukrainian SSR (1984), pp. 122–133.

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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 6, pp. 843–847, June, 1990.

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Eleiko, Y.I. Limiting distributions of time averages of additive functionals defined on a semi-Markov process. Ukr Math J 42, 744–747 (1990). https://doi.org/10.1007/BF01058927

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  • DOI: https://doi.org/10.1007/BF01058927

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