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

 

Modelling a solution of a hyperbolic equation with random initial conditions


Authors: Yu. V. Kozachenko and G. I. Slivka
Translated by: Oleg Klesov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 74 (2006).
Journal: Theor. Probability and Math. Statist. 74 (2007), 59-75
MSC (2000): Primary 60G35; Secondary 35L20
Published electronically: June 29, 2007
MathSciNet review: 2336779
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Abstract | References | Similar Articles | Additional Information

Abstract: A new method is proposed in this paper to construct models for solutions of boundary problems for hyperbolic equations with random initial conditions. We assume that initial conditions are strictly sub-Gaussian random fields (in particular, Gaussian random fields with zero mean). The models approximate solutions with a given accuracy and reliability in the uniform metric.


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Additional Information

Yu. V. Kozachenko
Affiliation: Department of Probability Theory and Mathematical Statistics, Faculty for Mathematics and Mechanics, National Taras Shevchenko University, Glushkov Avenue, 6, Kyiv, 03127, Ukraine
Email: yvk@univ.kiev.ua

G. I. Slivka
Affiliation: Department of Mathematical Analysis, Faculty for Mathematics, Uzhgorod University, Pidgirna Street, 46, Uzhgorod, Ukraine
Email: kafmatan@univ.uzhgorod.ua

DOI: http://dx.doi.org/10.1090/S0094-9000-07-00698-9
PII: S 0094-9000(07)00698-9
Received by editor(s): February 14, 2005
Published electronically: June 29, 2007
Article copyright: © Copyright 2007 American Mathematical Society