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Approximation of solutions of the wave equation driven by a stochastic measure


Authors: V. M. Radchenko and N. O. Stefans’ka
Translated by: S. V. Kvasko
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 99 (2018).
Journal: Theor. Probability and Math. Statist. 99 (2019), 229-238
MSC (2010): Primary 60H15; Secondary 60H05, 60G57
DOI: https://doi.org/10.1090/tpms/1092
Published electronically: February 27, 2020
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Abstract: The mild solution of the wave equation driven by a general stochastic measure is considered. It is proved that solutions of this equation converge if paths of stochastic measures converge.


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Additional Information

V. M. Radchenko
Affiliation: Department of Mathematical Analysis, Faculty for Mechanics and Mathematics, Kyiv Taras Shevchenko National University, Volodymyrs’ka Street, 64/13, Kyiv 01601, Ukraine
Email: vradchenko@univ.kiev.ua

N. O. Stefans’ka
Affiliation: Department of Mathematical Analysis, Faculty for Mechanics and Mathematics, Kyiv Taras Shevchenko National University, Volodymyrs’ka Street, 64/13, Kyiv 01601, Ukraine
Email: neliastefanska@gmail.com

DOI: https://doi.org/10.1090/tpms/1092
Keywords: Stochastic measure, stochastic wave equation, mild solution, Fourier--Haar series
Received by editor(s): April 2, 2018
Published electronically: February 27, 2020
Article copyright: © Copyright 2020 American Mathematical Society