Modelling a solution of a hyperbolic equation with random initial conditions
Authors:
Yu. V. Kozachenko and G. I. Slivka
Translated by:
Oleg Klesov
Journal:
Theor. Probability and Math. Statist. 74 (2007), 59-75
MSC (2000):
Primary 60G35; Secondary 35L20
DOI:
https://doi.org/10.1090/S0094-9000-07-00698-9
Published electronically:
June 29, 2007
MathSciNet review:
2336779
Full-text PDF Free Access
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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
- V. V. Buldygin and Yu. V. Kozachenko, Metric characterization of random variables and random processes, Translations of Mathematical Monographs, vol. 188, American Mathematical Society, Providence, RI, 2000. Translated from the 1998 Russian original by V. Zaiats. MR 1743716
- Yu. V. Kozachenko and A. O. Pashko, Modelling Stochastic Processes, “Kyiv University”, Kyiv, 1999. (Ukrainian)
- Yu. V. Kozachenko and G. Ī. Slivka, Justification of the Fourier method for a hyperbolic equation with random initial conditions, Teor. Ĭmovīr. Mat. Stat. 69 (2003), 63–78 (Ukrainian, with Ukrainian summary); English transl., Theory Probab. Math. Statist. 69 (2004), 67–83 (2005). MR 2110906, DOI https://doi.org/10.1090/S0094-9000-05-00615-0
- Nikolaĭ Sergeevič Košlyakov, M. M. Smirnov, and E. B. Gliner, Differential equations of mathematical physics, North-Holland Publishing Co., Amsterdam; Interscience Publishers John Wiley and Sons New York, 1964. Translated by Scripta Technica, Inc.; translation editor: Herbert J. Eagle. MR 0177179
- G. N. Polozhiĭ, Equations of Mathematical Physics, “Vysshaya shkola”, Moscow, 1964. (Russian)
References
- V. V. Buldygin and Yu. V. Kozachenko, Metric Characterization of Random Variables and Random Processes, AMS, Providence, Rhode Island, 2000. MR 1743716 (2001g:60089)
- Yu. V. Kozachenko and A. O. Pashko, Modelling Stochastic Processes, “Kyiv University”, Kyiv, 1999. (Ukrainian)
- 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)
- N. S. Koshlyakov, E. B. Gliner, and M. M. Smirnov, Differential Equations of Mathematical Physics, Moscow, “Vysshaya shkola”, 1970; English transl., North-Holland Publ. Co, Amsterdam, 1964. MR 0177179 (31:1443)
- G. N. Polozhiĭ, Equations of Mathematical Physics, “Vysshaya shkola”, Moscow, 1964. (Russian)
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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
Received by editor(s):
February 14, 2005
Published electronically:
June 29, 2007
Article copyright:
© Copyright 2007
American Mathematical Society
