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Probl. Peredachi Inf., 2012, Volume 48, Issue 2, Pages 48–64 (Mi ppi2074)  

Methods of Signal Processing

On frequency estimation for a periodic ergodic diffusion process

R. Höpfnera, Yu. A. Kutoyantsb

a Institut für Mathematik, Johannes Gutenberg Universität, Mainz, Germany
b Laboratoire de Statistique et Processus, Université du Maine, Le Mans, France

Abstract: We consider the problem of frequency estimation by observations for a periodic diffusion process possessing ergodic properties in two different situations. The first corresponds to a trend coefficient continuously differentiable with respect to parameter, and the second, to a discontinuous trend coefficient. It is shown that in the first case the maximum likelihood and Bayesian estimators are asymptotically normal with rate $T^{3/2}$, and in the second case these estimators have different limit distributions with rate $T^2$.

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English version:
Problems of Information Transmission, 2012, 48:2, 127–141

Bibliographic databases:

UDC: 621.391.1+519.2
Received: 08.08.2011

Citation: R. Höpfner, Yu. A. Kutoyants, “On frequency estimation for a periodic ergodic diffusion process”, Probl. Peredachi Inf., 48:2 (2012), 48–64; Problems Inform. Transmission, 48:2 (2012), 127–141

Citation in format AMSBIB
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\by R.~H\"opfner, Yu.~A.~Kutoyants
\paper On frequency estimation for a~periodic ergodic diffusion process
\jour Probl. Peredachi Inf.
\yr 2012
\vol 48
\issue 2
\pages 48--64
\mathnet{http://mi.mathnet.ru/ppi2074}
\transl
\jour Problems Inform. Transmission
\yr 2012
\vol 48
\issue 2
\pages 127--141
\crossref{https://doi.org/10.1134/S0032946012020032}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84865772828}


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