Fourier series and Fourier--Haar series for stochastic measures

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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Bibliographic Details
Published in:Theory of probability and mathematical statistics 2018, Vol.96, p.159-167
Main Authors: V. M. Radchenko, N. O. Stefans'ka
Format: Article
Language:English
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Summary: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.
ISSN:0094-9000
1547-7363
DOI:10.1090/tpms/1041