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Fundam. Prikl. Mat., 1996, Volume 2, Issue 4, Pages 1029–1043 (Mi fpm197)  

This article is cited in 3 scientific papers (total in 3 papers)

Research Papers Dedicated to the Memory of B. V. Gnedenko

Transient dynamics of two interacting random strings

A. A. Zamyatin, A. A. Yambartsev

M. V. Lomonosov Moscow State University

Abstract: A finite string is just a sequence of symbols from finite alphabet. We consider a Markov chain with the state space equal to the set of all pairs of strings. Transition probabilities depend only on $d$ leftmost symbols in each string. Besides that, the jumps of the chain are bounded: the lengths of strings at subsequent moments of time cannot differ by more than some $d$. We consider the case when dynamics of Markov chain is transient, i.e. as $t\to\infty$ the lengths of both strings tend to infinity with probability 1. In this situation we prove stabilization law: the distribution of symbols close to left ends of strings tends to those of some random process.

Full text: PDF file (561 kB)

Bibliographic databases:
UDC: 519.217
Received: 01.03.1996

Citation: A. A. Zamyatin, A. A. Yambartsev, “Transient dynamics of two interacting random strings”, Fundam. Prikl. Mat., 2:4 (1996), 1029–1043

Citation in format AMSBIB
\Bibitem{ZamYam96}
\by A.~A.~Zamyatin, A.~A.~Yambartsev
\paper Transient dynamics of two interacting random strings
\jour Fundam. Prikl. Mat.
\yr 1996
\vol 2
\issue 4
\pages 1029--1043
\mathnet{http://mi.mathnet.ru/fpm197}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1785770}
\zmath{https://zbmath.org/?q=an:0916.60057}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. A. Malyshev, “Interacting strings of symbols”, Russian Math. Surveys, 52:2 (1997), 299–326  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    2. A. A. Zamyatin, A. A. Yambartsev, “Classification of two interacting strings of symbols”, Russian Math. Surveys, 56:3 (2001), 597–598  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    3. Yambartsev, AA, “A stabilization law for two semi-infinite interacting strings of characters”, Bulletin of the Brazilian Mathematical Society, 34:3 (2003), 361  crossref  mathscinet  zmath  isi
  • Фундаментальная и прикладная математика
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