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Theory of Probability and Mathematical Statistics

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Wave equation with a stochastic measure


Author: I. M. Bodnarchuk
Translated by: N. Semenov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 94 (2016).
Journal: Theor. Probability and Math. Statist. 94 (2017), 1-16
MSC (2010): Primary 60H15; Secondary 60G17, 60G57
DOI: https://doi.org/10.1090/tpms/1005
Published electronically: August 25, 2017
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Abstract: The Cauchy problem for the wave equation on the line driven by a general stochastic measure is studied. The existence, uniqueness, and Hölder regularity of the mild solution are proved. The continuous dependence of the solution on the data is established.


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Additional Information

I. M. Bodnarchuk
Affiliation: Department of Mathematical Analysis, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue, 6, Kyiv 03127, Ukraine
Email: robeiko_i@ukr.net

DOI: https://doi.org/10.1090/tpms/1005
Keywords: Stochastic measure, stochastic wave equation, mild solution, H\"older condition, Besov space
Received by editor(s): April 5, 2016
Published electronically: August 25, 2017
Article copyright: © Copyright 2017 American Mathematical Society

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