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Theory of Probability and Mathematical Statistics
Theory of Probability and Mathematical Statistics
ISSN 1547-7363(online) ISSN 0094-9000(print)

   

 

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
Published electronically: January 11, 2013
MathSciNet review: 2933702
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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: http://dx.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