Theory of Probability and Mathematical Statistics

Author(s): Yu. V. Kozachenko; G. I. Slivka
Translated by: Oleg Klesov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, vipusk 74 (2006).
Journal: Theor. Probability and Math. Statist. No. 74 (2007), 59-75.
MSC (2000): Primary 60G35; Secondary 35L20
Posted: June 29, 2007
Retrieve article in: PDF DVI PostScript

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.

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)
4.: 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)
5.: G. N. Polozhi ${\u{\i\/}}\kern.15em$ , Equations of Mathematical Physics, ``Vysshaya shkola'', Moscow, 1964. (Russian)

Retrieve articles in Theory of Probability and Mathematical Statistics with MSC (2000): 60G35, 35L20

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: 10.1090/S0094-9000-07-00698-9
PII: S 0094-9000(07)00698-9
Received by editor(s): 14/FEB/2005
Posted: June 29, 2007
Copyright of article: Copyright 2007, American Mathematical Society

			Journals Home Search Author Info Subscribe Tech Support Help
ISSN: 1547-7363(e) 0094-9000(p)

Previous number \| Table of contents \| Next number Recently posted articles \| Most recent number \| All numbers Previous Article \| Next Article


	Comments: webmaster@ams.org © Copyright 2008, American Mathematical Society Privacy Statement		Search the AMS