NDLI: Trace Approximations of Products of Truncated Toeplitz Operators

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Sahakyan, A. A. Ginovyan, M. S.
Copyright Year	2012
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 RieszBessel 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.
Starting Page	57
Ending Page	71
Page Count	15
File Format	PDF
ISSN	0040585X
DOI	10.1137/S0040585X97985236
e-ISSN	10957219
Journal	Theory of Probability & Its Applications (TPRBAU)
Issue Number	1
Volume Number	56
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2012-02-15
Access Restriction	Subscribed
Subject Keyword	spectral density continuous-time stationary process fractional RieszBessel motion truncated Toeplitz operator singularity trace approximation long-memory
Content Type	Text
Resource Type	Article
Subject	Statistics and Probability Statistics, Probability and Uncertainty

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