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Teor. Veroyatnost. i Primenen., 1983, Volume 28, Issue 4, Pages 789–794 (Mi tvp2232)  

Short Communications

Expectations of the moments of reaching the level by the range type functionals for Markov chain

Yu. P. Filonov

Kiev

Abstract: Let $S_0,S_1,…$ be a homogeneous Markov chain on the set of integers,
$$ \tau_N=\min\{n:\sup_{0\le i,j\le n}(S_i-S_j)\ge N\},\qquad\bar\tau_n=\min\{n:\operatorname{card}\{S_0,…,S_n\}=N\}. $$
Theorems on the asymptotical behaviour of $\mathbf M\tau_n$ and $\mathbf M\bar\tau_n$ are proved.

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English version:
Theory of Probability and its Applications, 1984, 28:4, 825–829

Bibliographic databases:

Received: 07.07.1979

Citation: Yu. P. Filonov, “Expectations of the moments of reaching the level by the range type functionals for Markov chain”, Teor. Veroyatnost. i Primenen., 28:4 (1983), 789–794; Theory Probab. Appl., 28:4 (1984), 825–829

Citation in format AMSBIB
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\by Yu.~P.~Filonov
\paper Expectations of the moments of reaching the level by the range type functionals for Markov chain
\jour Teor. Veroyatnost. i Primenen.
\yr 1983
\vol 28
\issue 4
\pages 789--794
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=726907}
\zmath{https://zbmath.org/?q=an:0561.60069|0534.60061}
\transl
\jour Theory Probab. Appl.
\yr 1984
\vol 28
\issue 4
\pages 825--829
\crossref{https://doi.org/10.1137/1128083}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1984TV66700019}


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