Parameter estimation in hyperbolic multichannel models

Article type: Research Article

Authors: Liu, W. | Lototsky, S.V.

Affiliations: Department of Mathematics, USC, Los Angeles, CA, USA. E-mails: {liu5, lototsky}@usc.edu, URL: http://www-rcf.usc.edu/~lototsky

Abstract: A multichannel model is considered, with each channel represented by a linear second-order stochastic equation with two unknown coefficients. The channels are interpreted as the Fourier coefficients of the solution of a stochastic hyperbolic equation with possibly unbounded damping. The maximum likelihood estimator of the coefficients is constructed using the information from a finite number of channels. Necessary and sufficient conditions are determined for the consistency of the estimator as the number of channels increases, while the observation time and noise intensity remain fixed.

Keywords: cylindrical Brownian motion, second-order stochastic equations, stochastic hyperbolic equations

DOI: 10.3233/ASY-2010-0992

Journal: Asymptotic Analysis, vol. 68, no. 4, pp. 223-248, 2010