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Teor. Veroyatnost. i Primenen., 2018, Volume 63, Issue 2, Pages 389–401 (Mi tvp5177)  

This article is cited in 1 scientific paper (total in 1 paper)

Short Communications

Fourier series expansion of stochastic measures

V. M. Radchenko

National Taras Shevchenko University of Kyiv, Faculty of Mechanics and Mathematics

Abstract: We consider processes of the form $\mu(t)=\mu((0,t])$, where $\mu$ is a $\sigma$-additive in probability stochastic set function. Convergence of a random Fourier series to $\mu(t)$ is proved, and the approximation of integrals with respect to $\mu$ using Fejèr sums is obtained. For this approximation, we prove the convergence of solutions of the heat equation driven by $\mu$.

Keywords: stochastic measure, random Fourier series, stochastic integral, stochastic heat equation, mild solution.

Funding Agency Grant Number
Alexander von Humboldt-Stiftung 1074615


DOI: https://doi.org/10.4213/tvp5177

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English version:
Theory of Probability and its Applications, 2018, 63:2, 318–326

Bibliographic databases:

Received: 20.06.2016
Revised: 17.12.2017
Accepted:15.01.2018

Citation: V. M. Radchenko, “Fourier series expansion of stochastic measures”, Teor. Veroyatnost. i Primenen., 63:2 (2018), 389–401; Theory Probab. Appl., 63:2 (2018), 318–326

Citation in format AMSBIB
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\pages 318--326
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  • https://doi.org/10.4213/tvp5177
  • http://mi.mathnet.ru/eng/tvp/v63/i2/p389

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. Radchenko, N. Stefans'ka, “Approximation of solutions of the stochastic wave equation by using the Fourier series”, Mod. Stoch. Theory Appl., 5:4 (2018), 429–444  crossref  mathscinet  isi  scopus
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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