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Theory of Probability and Mathematical Statistics

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Fourier transform of general stochastic measures


Authors: V. M. Radchenko and N. O. Stefans’ka
Translated by: N. Semenov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 94 (2016).
Journal: Theor. Probability and Math. Statist. 94 (2017), 151-158
MSC (2010): Primary 60G57, 60H15, 60H05
DOI: https://doi.org/10.1090/tpms/1015
Published electronically: August 25, 2017
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Abstract: The Fourier transform is defined for general stochastic measures in  $ \mathbb{R}^d$. The inversion theorem for this transform is proved and a connection to the convergence of stochastic integrals is established. An example of applications of this result is considered 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

DOI: https://doi.org/10.1090/tpms/1015
Keywords: Stochastic measure, Fourier transform of stochastic processes, weak convergence, stochastic heat equation
Received by editor(s): April 28, 2016
Published electronically: August 25, 2017
Article copyright: © Copyright 2017 American Mathematical Society