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ISSN 1547-7363(online) ISSN 0094-9000(print)
The wave equation in the three-dimensional space driven by a general stochastic measure
Authors:
I. M. Bodnarchuk and V. M. Radchenko
Translated by:
N. N. Semenov
Journal:
Theor. Probability and Math. Statist. 100 (2020), 43-60
MSC (2010):
Primary 60H15; Secondary 60G17, 60G57
DOI:
https://doi.org/10.1090/tpms/1097
Published electronically:
August 4, 2020
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: The Cauchy problem for the wave equation in the three-dimensional space driven by a general stochastic measure is studied. The existence and uniqueness of a mild solution are proved. The Hölder regularity of paths of a mild solution in time and spatial variables is obtained.
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Additional Information
I. M. Bodnarchuk
Affiliation:
Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty of Mechanics and Mathematics, Taras Shevchenko National University of Kyiv, Volodymyrs’ka Street, 64/13, Kyiv 01601, Ukraine
Email:
ibodnarchuk@univ.kiev.ua
V. M. Radchenko
Affiliation:
Department of Mathematical Analysis, Faculty of Mechanics and Mathematics, Taras Shevchenko National University of Kyiv, Volodymyrs’ka Street, 64/13, Kyiv 01601, Ukraine
Email:
vradchenko@univ.kiev.ua
Keywords:
Stochastic measure,
stochastic wave equation,
mild solution,
Hölder condition,
Besov space
Received by editor(s):
March 23, 2019
Published electronically:
August 4, 2020
Article copyright:
© Copyright 2020
American Mathematical Society