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Teoriya Veroyatnostei i ee Primeneniya, 1975, Volume 20, Issue 1, Pages 162–170 (Mi tvp3002)  

This article is cited in 5 scientific papers (total in 5 papers)

Short Communications

Asymptotic properties of the probability of the degeneration after time $t$ for semi-Markov processes of multiplication

G. Sh. Lev

Barnaul
Full-text PDF (392 kB) Citations (5)
Abstract: Let $Y(t)$ be the process defined by
1) $Y(0)=x$,
2) $Y(t)=x\prod\limits_{i=1}^{\nu(t)}\gamma_i-\sum\limits_{i=1}^{\nu(t)}\tau_i\gamma_i\dots\gamma_{\nu(t)}-\gamma(t)$ where $\{\tau_i\}_1^\infty$ and $\{\gamma_i\}_1^\infty$ are independent sequences of independent identically distributed positive random variables and
\begin{gather*} \nu(t)=\sup\biggl\{n\colon\sum_{i=1}^n\tau_i\le t\biggr\}, \\ \gamma(t)=t-\sum_{i=1}^{\nu(t)}\tau_i. \end{gather*}
Let
\begin{gather*} \zeta_x=\inf\{t\colon Y(t)\le0\mid Y(0)=x\}, \\ f(x,t)=\mathbf P(\zeta_x\ge t). \end{gather*}

In the paper, asymptotic properties of $f(x,t)$ for $x>0$ as $t\to\infty$ are studied.
Received: 15.01.1974
English version:
Theory of Probability and its Applications, 1975, Volume 20, Issue 1, Pages 161–169
DOI: https://doi.org/10.1137/1120016
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: G. Sh. Lev, “Asymptotic properties of the probability of the degeneration after time $t$ for semi-Markov processes of multiplication”, Teor. Veroyatnost. i Primenen., 20:1 (1975), 162–170; Theory Probab. Appl., 20:1 (1975), 161–169
Citation in format AMSBIB
\Bibitem{Lev75}
\by G.~Sh.~Lev
\paper Asymptotic properties of the probability of the degeneration after time $t$ for semi-Markov processes of multiplication
\jour Teor. Veroyatnost. i Primenen.
\yr 1975
\vol 20
\issue 1
\pages 162--170
\mathnet{http://mi.mathnet.ru/tvp3002}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=373050}
\zmath{https://zbmath.org/?q=an:0339.60093}
\transl
\jour Theory Probab. Appl.
\yr 1975
\vol 20
\issue 1
\pages 161--169
\crossref{https://doi.org/10.1137/1120016}
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  • https://www.mathnet.ru/eng/tvp/v20/i1/p162
  • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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