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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 | 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.

References [Enhancements On Off] (What's this?)

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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

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