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

Full-text PDF

Abstract | References | Similar Articles | Additional Information

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