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This article is cited in 6 scientific papers (total in 6 papers)
Trace approximations of products of truncated Toeplitz operators
M. S. Ginovyana, A. A. Sahakyanb a Boston University, Department of Mathematics and Statistics
b Department of Mathematics and Mechanics, Yerevan State University
Abstract:
The paper establishes error orders for integral limit approximations to the traces of products of truncated
Toeplitz operators generated by integrable real symmetric functions defined on the real line. These approximations and the corresponding error bounds are of importance in the statistical analysis of continuous-time stationary processes (asymptotic distributions and large deviations of Toeplitz type quadratic
functionals, estimation of the spectral parameters and functionals, etc.) An explicit second-order asymptotic expansion is found for the trace of a product of two truncated Toeplitz operators generated by the spectral densities of continuous-time stationary fractional Riesz-Bessel motions. The order of magnitude of the second term in this expansion is shown to depend on the long-memory parameters of the processes. Also, it is shown that the pole in the first-order approximation is removed by the second-order term, which provides a
substantially improved approximation to the original functional.
Keywords:
trace approximation, truncated Toeplitz operator, continuous-time stationary process, long-memory, spectral
density, singularity, fractional Riesz-Bessel motion.
Received: 20.01.2010
Citation:
M. S. Ginovyan, A. A. Sahakyan, “Trace approximations of products of truncated Toeplitz operators”, Teor. Veroyatnost. i Primenen., 56:1 (2011), 123–139; Theory Probab. Appl., 56:1 (2012), 57–71
Linking options:
https://www.mathnet.ru/eng/tvp4326https://doi.org/10.4213/tvp4326 https://www.mathnet.ru/eng/tvp/v56/i1/p123
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Abstract page: | 376 | Full-text PDF : | 169 | References: | 61 |
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