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 | References | Similar Articles | Additional Information

Abstract: The Fourier transform is defined for general stochastic measures in . 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