RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Archive Impact factor Subscription Guidelines for authors Submit a manuscript Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Teor. Veroyatnost. i Primenen.: Year: Volume: Issue: Page: Find

 Teor. Veroyatnost. i Primenen., 1972, Volume 17, Issue 3, Pages 583–588 (Mi tvp2672)

Short Communications

On convergence of semi-markov processes of multiplication with drift to a diffusion process

G. Sh. Lev

Barnaul

Abstract: A sequence of processes $Y_k(t)$, $t\ge0$, is considered, $Y_k(t)$ being of the form: $Y_k(0)=x$, $Y_k(t)$ are right continuous and $dY_k/dt=-1$ everywhere except at point $t_i^k=\sum_{l=1}^i\tau_{lk}$, where $Y_k(t_i^k)=\gamma_{ik}Y_k(t_i^k-0)$. Here $\{\tau_{ik}\}_{i=1}^\infty$, $\{\gamma_{ik}\}_{i=1}^\infty$ for any fixed $k$, are independent sequences of independent identically distributed positive random variables. It is proved that, under some restrictions on $\tau_{ik}$ and $\gamma_{ik}$, $Y_k(t)$converge to a diffusion process. The behaviour of this process as $t\to\infty$ is studied.

Full text: PDF file (283 kB)

English version:
Theory of Probability and its Applications, 1973, 17:3, 551–556

Bibliographic databases:

Citation: G. Sh. Lev, “On convergence of semi-markov processes of multiplication with drift to a diffusion process”, Teor. Veroyatnost. i Primenen., 17:3 (1972), 583–588; Theory Probab. Appl., 17:3 (1973), 551–556

Citation in format AMSBIB
\Bibitem{Lev72} \by G.~Sh.~Lev \paper On convergence of semi-markov processes of multiplication with drift to a~diffusion process \jour Teor. Veroyatnost. i Primenen. \yr 1972 \vol 17 \issue 3 \pages 583--588 \mathnet{http://mi.mathnet.ru/tvp2672} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=305492} \zmath{https://zbmath.org/?q=an:0299.60061} \transl \jour Theory Probab. Appl. \yr 1973 \vol 17 \issue 3 \pages 551--556 \crossref{https://doi.org/10.1137/1117067}