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Comparison theorems for the small ball probabilities of the Green Gaussian processes in weighted $ L_2$-norms


Authors: A. I. Nazarov and R. S. Pusev
Translated by: A. I. Nazarov
Original publication: Algebra i Analiz, tom 25 (2013), nomer 3.
Journal: St. Petersburg Math. J. 25 (2014), 455-466
MSC (2010): Primary 60G15
DOI: https://doi.org/10.1090/S1061-0022-2014-01299-X
Published electronically: May 16, 2014
MathSciNet review: 3184601
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Abstract | References | Similar Articles | Additional Information

Abstract: Comparison theorems are proved for small ball probabilities of the Green Gaussian processes in weighted $ L_2$-norms. The sharp small ball asymptotics are found for many classical processes under quite general assumptions on the weight.


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Additional Information

A. I. Nazarov
Affiliation: St. Petersburg Branch, Steklov Mathematical Institute, Russian Academy of Science, Fontanka 27, St. Petersburg 191023, Russia; St. Petersburg State University, Universitetskii pr. 28, St. Petersburg 198504, Russia
Email: al.il.nazarov@gmail.com

R. S. Pusev
Affiliation: St. Petersburg State University, Universitetskii pr. 28, St. Petersburg 198504, Russia
Email: Ruslan.Pusev@math.spbu.ru

DOI: https://doi.org/10.1090/S1061-0022-2014-01299-X
Keywords: Small ball probabilities, Gaussian processes, comparison theorems, spectral asymptotics
Received by editor(s): March 1, 2013
Published electronically: May 16, 2014
Additional Notes: The authors were supported by RFBR (grants nos. 10-01-00154 and 13-01-00172)
The first author was also supported by St. Petersburg State University grant 6.38.64.2012
The second author was also supported by St. Petersburg State University grant 6.38.672.2013, by the Chebyshev Laboratory of St. Petersburg State University with the Russian Government grant 11.G34.31.0026, and by the Program of supporting for Leading Scientific Schools (NSh-1216.2012.1).
Dedicated: Dedicated to Boris Mikhaĭlovich Makarov, with great admiration
Article copyright: © Copyright 2014 American Mathematical Society