Skip to main content
SpringerLink
Log in

Attainability property and ergodicity theorems for a semi-Markov process with an arbitrary set of states

  • Published:
Mathematical notes of the Academy of Sciences of the USSR Aims and scope Submit manuscript

Abstract

The connection is studied which exists between the finiteness of the average time to achieve certain subsets, on the one hand, and, on the other, the ergodic properties of the process. The assertions proven in this paper generalize results obtained for semi-Markov processes with discrete sets of states. Moreover, the connection is studied between the asymptotic time to achieve a set whose “dimensions” tend to zero and, on the other hand, the ergodicity of the process.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Literature cited

  1. A. P. Cherenkov, “Existence theorems for semi-Markov processes with arbitrary sets of states,” Mat. Zametki,15, No. 4, 621–630 (1974).

    Google Scholar 

  2. Kai Lai Chung, Markov Chains with Stationary Transition Probabilities, Springer-Verlag (1967).

  3. D. R. Cox and V. L. Smith, Renewal Theory, Halsted Press (1962).

  4. G. H. Hardy, Divergent Series, Oxford Univ. Press, Oxford (1949).

    Google Scholar 

  5. A. P. Cherenkov, “Additive functionals of semi-Markov processes with absorption,” Mat. Zametki,17, No. 2, 329–339 (1975).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. All-Union Research Institute for Chemical Means of Plant Protection, USSR

    A. P. Cherenkov

Authors
  1. A. P. Cherenkov
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Matematicheskie Zametki, Vol. 21, No. 3, pp. 301–312, March, 1977.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Cherenkov, A.P. Attainability property and ergodicity theorems for a semi-Markov process with an arbitrary set of states. Mathematical Notes of the Academy of Sciences of the USSR 21, 167–173 (1977). https://doi.org/10.1007/BF01106739

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01106739

Keywords

Search

Navigation