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ISSN 1547-7363(online) ISSN 0094-9000(print)
Fourier series and Fourier–Haar series for stochastic measures
Authors:
V. M. Radchenko and N. O. Stefans’ka
Translated by:
S. V. Kvasko
Journal:
Theor. Probability and Math. Statist. 96 (2018), 159-167
MSC (2010):
Primary 60G57, 60H15, 60H05
DOI:
https://doi.org/10.1090/tpms/1041
Published electronically:
October 5, 2018
MathSciNet review:
3666879
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: The Fourier series and Fourier–Haar series are introduced for general stochastic measures. The convergence of partial sums of these series and the absolute continuity of a stochastic measure are studied. An application is given for the convergence of solutions of the stochastic heat equation.
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Additional Information
V. M. Radchenko
Affiliation:
Department of Mathematical Analysis, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue, 6, Kyiv 03127, Ukraine
Email:
vradchenko@univ.kiev.ua
N. O. Stefans’ka
Affiliation:
Department of Mathematical Analysis, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue, 6, Kyiv 03127, Ukraine
Email:
valentinasavych@mail.ru
Keywords:
Stochastic measure,
Fourier series for stochastic measure,
Fourier–Haar series for stochastic measure,
stochastic heat equation
Received by editor(s):
December 7, 2016
Published electronically:
October 5, 2018
Article copyright:
© Copyright 2018
American Mathematical Society