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Theory of Probability and Mathematical Statistics

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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.

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

  • 1. V. V. Buldygin and Yu. V. Kozachenko, Metric Characterization of Random Variables and Random Processes, AMS, Providence, Rhode Island, 2000. MR 1743716 (2001g:60089)
  • 2. Yu. V. Kozachenko and A. O. Pashko, Modelling Stochastic Processes, ``Kyiv University'', Kyiv, 1999. (Ukrainian)
  • 3. Yu. V. Kozachenko and G. I. Slivka, Justification of the Fourier method for hyperbolic equations with random initial conditions, Teor. Imovirnost. Matem. Statist. 69 (2003), 63-78; English transl. in Theory Probab. Mathem. Statist. 69 (2004), 67-83. MR 2110906 (2005k:60127)
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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

G. I. Slivka
Affiliation: Department of Mathematical Analysis, Faculty for Mathematics, Uzhgorod University, Pidgirna Street, 46, Uzhgorod, Ukraine

Received by editor(s): February 14, 2005
Published electronically: June 29, 2007
Article copyright: © Copyright 2007 American Mathematical Society

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