Email this article On Spectral Asymptotics for a Family of Finite-Dimensional Perturbations of Operators of Trace Class
- Authors: Petrova Y.P.1
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Affiliations:
- St. Petersburg State University
- Issue: Vol 98, No 1 (2018)
- Pages: 367-369
- Section: Mathematics
- URL: https://journals.rcsi.science/1064-5624/article/view/225536
- DOI: https://doi.org/10.1134/S1064562418050204
- ID: 225536
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Abstract
Spectral asymptotics for a family of finite-dimensional perturbations of operators of trace class are found. The results are used to find exact asymptotics of small ball probabilities in the Hilbert norm for finitedimensional perturbations of Gaussian functions. As an example, Durbin processes appearing in the study of empirical processes with estimated parameters are considered.
About the authors
Yu. P. Petrova
St. Petersburg State University
Author for correspondence.
Email: yu.pe.petrova@yandex.ru
Russian Federation, St. Petersburg
