On the existence and uniqueness of solutions of the Cauchy problem for wave equations with general stochastic measures

Author:
D. M. Gorodnya

Translated by:
S. Kvasko

Original publication:
Teoriya Imovirnostei ta Matematichna Statistika, tom **85** (2011).

Journal:
Theor. Probability and Math. Statist. **85** (2012), 53-59

MSC (2010):
Primary 60G57, 60H15, 60H05, 35L05, 46F99

DOI:
https://doi.org/10.1090/S0094-9000-2013-00873-4

Published electronically:
January 11, 2013

MathSciNet review:
2933702

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The existence and uniqueness of a solution of the Cauchy problem for wave equations containing a term expressed via the integral with respect to a stochastic measure are proved. Some general properties of generalized functions assuming values in a Fréchet space are used in the proof of the uniqueness of a solution.

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Additional Information

**D. M. Gorodnya**

Affiliation:
Department of Mathematical Analysis, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue, 4e, Kiev 03127, Ukraine

Email:
gorodnyaya@yandex.ru

DOI:
https://doi.org/10.1090/S0094-9000-2013-00873-4

Keywords:
Stochastic wave equation,
Cauchy problem,
stochastic measure,
Fréchet space,
generalized function

Received by editor(s):
June 23, 2011

Published electronically:
January 11, 2013

Article copyright:
© Copyright 2013
American Mathematical Society