Skip to main content
Log in

Time intervals of constant sojourn of a homogeneous Markov chain in a fixed subset of states

  • Published:
Siberian Mathematical Journal Aims and scope Submit manuscript

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

Access this article

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

Instant access to the full article PDF.

Literature Cited

  1. V. L. Goncharov, “From the domain of combinatorics,” Izv. Akad. Nauk SSSR, Ser. Mat.,8, No. 1, 3–48 (1944).

    Google Scholar 

  2. P. Erdös and P. Révész, “On the length of the longest head-run,” Topics in Information Theory (Second Colloq., Keszthely, 1975), Colloq. Soc. János Bolyai, Vol. 16, North-Holland, Amsterdam (1977), pp. 219–228.

    Google Scholar 

  3. L. Ya. Savel'ev, “Long runs in Markov sequences,” Tr. Inst. Mat. Sib. Otd. Akad. Nauk SSSR,5, 137–144 (1985).

    Google Scholar 

  4. S. S. Samarova, “On the number of time intervals that an ergodic Markov chain is continuously in a fixed state,” Dokl. Akad. Nauk SSSR,260, No. 1, 35–40 (1981).

    Google Scholar 

  5. S. S. Samarova, “On certain properties of ergodic Markov chains that are satisfied with probability one,” Author's Abstract of Candidate's Dissertation, Moscow (1981).

  6. N. Kusolitsch, “Longest runs in Markov chains,” in: Probability and Statistical Inference (Bad Tatzmannsdorf, 1981), Reidel, Dordrecht-Boston, Mass. (1982), pp. 223–230.

    Google Scholar 

  7. S. Yu. Novak, “On the length of the largest series of successes in Markov chains,” in: Fourth International Vilnius Conference on Probability Theory and Mathematical Statistics. Abstracts of Communications, Akad. Nauk Lit. SSR, Inst. Mat. i Kibernet., Vilnius (1985), pp. 267–268.

    Google Scholar 

  8. A. Renyi, Probability Theory, North-Holland, Amsterdam (1970).

    Google Scholar 

  9. V. V. Anisimov and A. N. Chernyak, “Limit theorems for certain rare functionals on Markov chains and semi-Markov processes,” Teor. Veroyatn. Mat. Statist.,26, 3–8 (1982).

    Google Scholar 

  10. A. A. Borovkov, Mathematical Statistics [in Russian], Nauka, Moscow (1984).

    Google Scholar 

Download references

Authors

Additional information

Novosibirsk. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 29, No. 1, pp. 129–140, January–February, 1988.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Novak, S.Y. Time intervals of constant sojourn of a homogeneous Markov chain in a fixed subset of states. Sib Math J 29, 100–109 (1988). https://doi.org/10.1007/BF00975021

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00975021

Keywords

Navigation