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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
Published electronically: February 8, 2005
MathSciNet review: 2110906
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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.

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  • 1. 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
  • 2. M. A. Krasnosel′skiĭ and Ja. B. Rutickiĭ, Vypuklye funktsii i prostranstva Orlicha, Problems of Contemporary Mathematics, Gosudarstv. Izdat. Fiz.-Mat. Lit., Moscow, 1958 (Russian). MR 0106412
  • 3. Yu. V. Kozachenko and Yu. A. Koval′chuk, Boundary value problems with random initial conditions, and functional series from 𝑠𝑢𝑏ᵩ(Ω). I, Ukraïn. Mat. Zh. 50 (1998), no. 4, 504–515 (Russian, with English and Ukrainian summaries); English transl., Ukrainian Math. J. 50 (1998), no. 4, 572–585 (1999). MR 1698149, 10.1007/BF02487389
  • 4. O. N. Gladkaja, Conditions for the directional differentiability of sample functions of random fields, Teor. Verojatnost. i Mat. Statist. Vyp. 17 (1977), 33–41, 164 (Russian, with English summary). MR 0451375
  • 5. Yu. Kozachenko, O. Vasylyk, and T. Sottinen, Path space large deviations of a large buffer with Gaussian input traffic, Queueing Syst. 42 (2002), no. 2, 113–129. MR 1932123, 10.1023/A:1020161203956
  • 6. N. S. Košljakov, È. B. Gliner, and M. M. Smirnov, Differentsialnye uravneniya matematicheskoi fiziki, Edited by N. S. Košljakov, Gosudarstv. Izdat. Fiz.-Mat. Lit., Moscow, 1962 (Russian). MR 0158145
  • 7. Yu. V. Kozachenko, Local properties of trajectories of some random functions, Ukr. Matem. Zh. 17 (1977), 33-40. (Russian)
  • 8. Ganna Ī. Slivka, Justification of the application of the Fourier method to the problem of the vibration of a round membrane with random initial conditions, Vīsn. Kiïv. Unīv. Ser. Fīz.-Mat. Nauki 4 (2002), 31–37 (Ukrainian, with English and Ukrainian summaries). 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

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

Received by editor(s): March 28, 2003
Published electronically: February 8, 2005
Article copyright: © Copyright 2005 American Mathematical Society