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Teor. Veroyatnost. i Primenen., 1968, Volume 13, Issue 2, Pages 326–332 (Mi tvp849)  

This article is cited in 1 scientific paper (total in 1 paper)

Short Communications

Confidence limits for the parameter $\lambda$ of a complex stationary Gaussian Markovian process

M. Arató

Budapest

Abstract: Let $\zeta(t)=\xi(t)+t\eta(t)$ be complex process satisfying the stochastic differential equation (1.1)
$$ d\zeta(t)=-\gamma\zeta(t) dt+d\chi(t), $$
where $y=\lambda-i\omega$, $\chi(t)=\varphi(t)+i\psi(t)$, $\varphi$ and $\psi$ are independent Wiener processes. We get the characteristic function (2.2) of the sufficient statistics $s_1^2$, $Ts_2^2$ of the unknown parameter $\varkappa=\lambda T$. The quantiles of the distribution function of the maximum likelihood estimator $\widehat\varkappa=\widehat\lambda T$ (see (2.1)) at the levels $p=0.999$; $0.99$; $0.975$; $0.95$; $0.90$; $0.10$; $0.05$; $0.025$; $0.01$; $0.001$ are tabulated. From here we can get the confidence limits for the parameter $\varkappa=\lambda T$ ($0.1<\varkappa\le100$).

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English version:
Theory of Probability and its Applications, 1968, 13:2, 314–320

Bibliographic databases:

Received: 02.09.1966

Citation: M. Arató, “Confidence limits for the parameter $\lambda$ of a complex stationary Gaussian Markovian process”, Teor. Veroyatnost. i Primenen., 13:2 (1968), 326–332; Theory Probab. Appl., 13:2 (1968), 314–320

Citation in format AMSBIB
\Bibitem{Ara68}
\by M.~Arat\'o
\paper Confidence limits for the parameter $\lambda$ of a~complex stationary Gaussian Markovian process
\jour Teor. Veroyatnost. i Primenen.
\yr 1968
\vol 13
\issue 2
\pages 326--332
\mathnet{http://mi.mathnet.ru/tvp849}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=253497}
\zmath{https://zbmath.org/?q=an:0181.44804|0174.50202}
\transl
\jour Theory Probab. Appl.
\yr 1968
\vol 13
\issue 2
\pages 314--320
\crossref{https://doi.org/10.1137/1113035}


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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. Arato M., Baran S., Ispany M., “Functionals of complex Ornstein–Uhlenbeck processes”, Computers & Mathematics With Applications, 37:1 (1999), 1–13  crossref  mathscinet  zmath  isi
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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