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Teoriya Veroyatnostei i ee Primeneniya, 1976, Volume 21, Issue 3, Pages 620–628
(Mi tvp3406)
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Short Communications
On the convergence of discrete schemes to continuous ones in some problems of sequential analysis
M. J. Kel'bert Moscow
Abstract:
Two problems of sequential analysis are considered in the paper: the problem of «disorder» and the problem of sequential testing statistical hypotheses.
Let the observations at moments $k\Delta$ ($k=0,1,\dots,T/\Delta$), $\Delta\to 0$, are available, while the hypotheses considered get closer to each other. It is shown that the statistics $\pi_{\Delta}(t)$ and $\varphi_{\Delta}(t)$ converge to the diffusion processes $\pi(t)$ and $\varphi(t)$ (Lemmas 2–4) as $\Delta\to 0$. Conditions are also given (Theorems 2, 3) under which the convergence of the average lag time in the problem of «disorder» and the convergence of $\mathbf M_0\tau^{\Delta}$ and $\mathbf M_1\tau^{\Delta}$ in the problem of sequential testing statistical hypothesis follows from the convergence of these statistics.
Received: 27.01.1975
Citation:
M. J. Kel'bert, “On the convergence of discrete schemes to continuous ones in some problems of sequential analysis”, Teor. Veroyatnost. i Primenen., 21:3 (1976), 620–628; Theory Probab. Appl., 21:3 (1977), 605–614
Linking options:
https://www.mathnet.ru/eng/tvp3406 https://www.mathnet.ru/eng/tvp/v21/i3/p620
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Abstract page: | 158 | Full-text PDF : | 82 |
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