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Teoriya Veroyatnostei i ee Primeneniya, 1994, Volume 39, Issue 4, Pages 669–680 (Mi tvp3846)  
On the problem of detecting random trajectories

I. M. Arbekov, V. I. Vinokurov, B. V. Ryazanov
Full-text PDF (554 kB)
Abstract: A consistent test is constructed for the hypothesis that there is a particle which performs random walk along the integer lattice of the real line and carries a “useful signal” in the presence of “noise”. The limiting form of the linear approximation to the likelihood ratio is found to be a convolution of the standard normal distribution and a functional of the standard Wiener process.
Keywords: likelihood ratio statistics, random walk, signal detection in the presence of noise, functional of a Wiener process, problem of detection of random trajectories.
Received: 08.04.1991
English version:
Theory of Probability and its Applications, 1994, Volume 39, Issue 4, Pages 547–557
DOI: https://doi.org/10.1137/1139042
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: I. M. Arbekov, V. I. Vinokurov, B. V. Ryazanov, “On the problem of detecting random trajectories”, Teor. Veroyatnost. i Primenen., 39:4 (1994), 669–680; Theory Probab. Appl., 39:4 (1994), 547–557
Citation in format AMSBIB
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\paper On the problem of detecting random trajectories
\jour Teor. Veroyatnost. i Primenen.
\yr 1994
\vol 39
\issue 4
\pages 669--680
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\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1347645}
\zmath{https://zbmath.org/?q=an:0838.62076}
\transl
\jour Theory Probab. Appl.
\yr 1994
\vol 39
\issue 4
\pages 547--557
\crossref{https://doi.org/10.1137/1139042}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1995TR71500002}
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