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Theory of Probability and Mathematical Statistics

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Justification of the Fourier method for hyperbolic equations with random initial conditions


Authors: Yu. V. Kozachenko and G. I. Slivka
Translated by: Oleg Klesov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 69 (2003).
Journal: Theor. Probability and Math. Statist. 69 (2004), 67-83
MSC (2000): Primary 60G35; Secondary 35L20
DOI: https://doi.org/10.1090/S0094-9000-05-00615-0
Published electronically: February 8, 2005
MathSciNet review: 2110906
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Abstract | References | Similar Articles | Additional Information

Abstract: Conditions for the existence of a twice differentiable solution of a hyperbolic type partial differential equation with random strongly $\operatorname{Sub}_{\varphi}(\Omega)$ initial conditions are found in the multidimensional case.


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

  • 1. V. V. Buldygin and Yu. V. Kozachenko, Metric Characterization of Random Variables and Random Processes, Amer. Math. Soc., Providence, RI, 2000. MR 1743716 (2001g:60089)
  • 2. M. A. Krasnosel'ski{\u{\i}}\kern.15em and Ya. B. Ruticki{\u{\i}}\kern.15em, Convex Functions and Orlicz Spaces, Fizmatgiz, Moscow, 1958; English transl., Noordhof, Gröningen, 1961. MR 0106412 (21:5144)
  • 3. Yu. V. Kozachenko and Yu. A. Koval'chuk, Boundary value problems with random initial conditions and series of functions of $\Sub_\varphi(\Omega)$, Ukr. Matem. Zh. 50 (1998), no. 4, 504-515; English transl. in Ukrainian Math. J. 50 (1998), no. 4, 572-585 (1999). MR 1698149 (2000f:60029)
  • 4. O. N. Gladkaya, Conditions for directional differentiability of the sample functions of random fields, Teor. Veroyatnost. Matem. Statist. 17 (1977), 33-40; English transl. in Theory Probab. Mathem. Statist. 17 (1977), 35-43. MR 0451375 (56:9661)
  • 5. Yu. V. Kozachenko, O. Vasylyk, and T. Sottinen, Path space large deviations of a large buffer with Gaussian input traffic, Queueing System 42 (2002), no. 2, 113-129. MR 1932123 (2004a:60149)
  • 6. N. S. Koshlyakov, E. B. Gliner, and M. M. Smirnov, Differential Equations of Mathematical Physics, ``Vysshaya Shkola'', Moscow, 1962; English transl., North-Holland, Amsterdam, 1964. MR 0158145 (28:1371)
  • 7. Yu. V. Kozachenko, Local properties of trajectories of some random functions, Ukr. Matem. Zh. 17 (1977), 33-40. (Russian)
  • 8. G. I. Slivka, Justification of the application of the Fourier method to the problem of the vibration of a round membrane with random initial conditions, Visn. Kyïv Univ. Ser. Fiz.-Mat. Nauk 4 (2002), 31-37. (Ukrainian) MR 1972945
  • 9. G. I. Slivka, A boundary value problem of the mathematical physics with random initial conditions, Visn. Kyïv Univ. Ser. Fiz.-Mat. Nauk 5 (2002), 172-178. (Ukrainian)

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Additional Information

Yu. V. Kozachenko
Affiliation: Department of Probability Theory and Mathematical Statistics, Faculty for Mechanics and Mathematics, Kyiv National Taras Shevchenko University, Academician 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: aslyvka@yahoo.com

DOI: https://doi.org/10.1090/S0094-9000-05-00615-0
Received by editor(s): March 28, 2003
Published electronically: February 8, 2005
Article copyright: © Copyright 2005 American Mathematical Society

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