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St. Petersburg Mathematical Journal

This journal is a cover-to-cover translation into English of Algebra i Analiz, published six times a year by the mathematics section of the Russian Academy of Sciences.

ISSN 1547-7371 (online) ISSN 1061-0022 (print)

The 2020 MCQ for St. Petersburg Mathematical Journal is 0.68.

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Comparison theorems for the small ball probabilities of the Green Gaussian processes in weighted $L_2$-norms
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by A. I. Nazarov and R. S. Pusev
Translated by: A. I. Nazarov
St. Petersburg Math. J. 25 (2014), 455-466
DOI: https://doi.org/10.1090/S1061-0022-2014-01299-X
Published electronically: May 16, 2014
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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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Bibliographic 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
  • MR Author ID: 228194
  • 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
  • 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
  • © Copyright 2014 American Mathematical Society
  • Journal: St. Petersburg Math. J. 25 (2014), 455-466
  • MSC (2010): Primary 60G15
  • DOI: https://doi.org/10.1090/S1061-0022-2014-01299-X
  • MathSciNet review: 3184601