The heat equation with random initial conditions from Orlicz spaces
Authors:
Yu. V. Kozachenko and K. I. Veresh
Translated by:
Oleg Klesov
Original publication:
Teoriya Imovirnostei ta Matematichna Statistika, tom 80 (2009).
Journal:
Theor. Probability and Math. Statist. 80 (2010), 7184
MSC (2000):
Primary 60G60, 60G17
Published electronically:
August 19, 2010
MathSciNet review:
2541953
Fulltext PDF Free Access
Abstract 
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Additional Information
Abstract: Conditions for justification of the Fourier method for parabolic equations with random initial conditions from Orlicz spaces of random variables are obtained. Bounds for the distribution of the supremum of solutions of such equations are found.
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Ī. Slivka, Justification of the Fourier method
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Ĭmovīr. Mat. Stat. 69 (2003), 63–78
(Ukrainian, with Ukrainian summary); English transl., Theory Probab. Math. Statist. 69 (2004), 67–83 (2005). MR 2110906
(2005k:60127), 10.1090/S0094900005006150
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V. Kozachenko and M.
M. Perestyuk, On the uniform convergence of wavelet expansions of
random processes from Orlicz spaces of random variables. I,
Ukraïn. Mat. Zh. 59 (2007), no. 12,
1647–1660 (Ukrainian, with English and Russian summaries); English
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I. G. Polozhyĭ, Equations of Mathematical Physics, Vysshaya Shkola, Moscow, 1964. (Russian)
 1.
 V. V. Buldygin and Yu. V. Kozachenko, On an applicability of the Fourier method for solving problems with random boundary conditions, Random Processes in the Problems of Mathematical Physics, Institute of Mathematics, Academy of Science of Ukr. SSR, Kiev, 1979, pp. 435. (Russian) MR 587658 (83i:35080)
 2.
 E. Beĭsenbaev and Yu. V. Kozachenko, Uniform convergence of random series in probability and the solution of boundaryvalue problems with random initial conditions, Teor. Imovir. Mat. Stat. 21 (1979), 923; English transl. in Theory Probab. Math. Statist. 21 (1980), 924. MR 550238 (81g:60036)
 3.
 V. V. Buldygin and Yu. V. Kozachenko, Metric Characterization of Random Variables and Random Processes, TViMS, Kiev, 1998; English transl., Translations of Math. Mono., vol. 188, American Mathematical Society, Providence, RI, 2000. MR 1743716 (2001g:60089)
 4.
 B. V. Dovgay, Yu. V. Kozachenko, and G. I. SlyvkaTylyshchak, BoundaryValue Problems of Mathematical Physics with Random Factors, Kyiv University, Kyiv, 2008. (Ukrainian)
 5.
 E. Barrasa de la Krus and Yu. V. Kozachenko, Boundaryvalue problems for equations of mathematical physics with strictly Orlicz random initial conditions, Random Oper. Stoch. Eq. 3 (1995), no. 3, 201220. MR 1354813 (96h:60009)
 6.
 Yu. V. Kozachenko and G. I. Slivka, Justification of the Fourier method for hyperbolic equations with random initial conditions, Teor. Imovir. Mat. Stat. 69 (2003), 6378; English transl. in Theory Probab. Math. Statist. 69 (2004), 6783. MR 2110906 (2005k:60127)
 7.
 Yu. V. Kozachenko and M. M. Perestyuk, On the uniform convergence of wavelet expansions of random processes belonging to the Orlicz spaces of random variables. I, Ukr. Matem. Zh. 59 (2007), no. 12, 16471659; English transl. in Ukrain. Math. J. 59 (2007), no. 12, 18501869. MR 2411593 (2009b:60058)
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 I. G. Polozhyĭ, 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 Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue, 2, Kiev 03127, Ukraine
Email:
yvk@univ.kiev.ua
K. I. Veresh
Affiliation:
Department of Probability Theory and Mathematical Statistics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue, 2, Kiev 03127, Ukraine
Email:
yvk@univ.kiev.ua
DOI:
http://dx.doi.org/10.1090/S009490002010007952
Keywords:
Parabolic equations,
Orlicz spaces
Received by editor(s):
February 2, 2009
Published electronically:
August 19, 2010
Article copyright:
© Copyright 2010
American Mathematical Society
