Advertisement

Siberian Mathematical Journal

, Volume 29, Issue 1, pp 100–109 | Cite as

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

  • S. Yu. Novak
Article

Keywords

Markov Chain Homogeneous Markov Chain Fixed Subset Constant Sojourn 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature Cited

  1. 1.
    V. L. Goncharov, “From the domain of combinatorics,” Izv. Akad. Nauk SSSR, Ser. Mat.,8, No. 1, 3–48 (1944).Google Scholar
  2. 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. 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. 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. 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).Google Scholar
  6. 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. 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. 8.
    A. Renyi, Probability Theory, North-Holland, Amsterdam (1970).Google Scholar
  9. 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. 10.
    A. A. Borovkov, Mathematical Statistics [in Russian], Nauka, Moscow (1984).Google Scholar

Copyright information

© Plenum Publishing Corporation 1988

Authors and Affiliations

  • S. Yu. Novak

There are no affiliations available

Personalised recommendations