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Random Operators and Stochastic Equations

Editor-in-Chief: Girko, Vyacheslav

Managing Editor: Molchanov, S.

Editorial Board Member: Accardi, L. / Albeverio, Sergio / Carmona, R. / Casati, G. / Christopeit, N. / Domanski, C. / Drygas, Hilmar / Gupta, A.K. / Ibragimov, I. / Kirsch, Werner / Klein, A. / Kondratyev, Yuri / Kurotschka, V. / Leonenko, N. / Loubaton, Philippe / Orsingher, E. / Pastur, L. / Rodrigues, Waldyr A. / Shiryaev, Albert / Turbin, A.F. / Veretennikov, Alexandre

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CiteScore 2016: 0.37

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1569-397X
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Volume 22, Issue 1 (Mar 2014)

Issues

The Cauchy problem for the heat equation with a random right side

Yuriy V. Kozachenko
  • Department of Probability Theory, Statistics and the Mathematics of Risk, Faculty of Mechanics and Mathematics, Taras Shevchenko National University, Academician Glushkov Avenue 2, 03127, Kyiv, Ukraine
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/ Anna I. Slyvka-Tylyshchak
  • Department of Probability Theory, Statistics and the Mathematics of Risk, Faculty of Mechanics and Mathematics, Taras Shevchenko National University, Academician Glushkov Avenue 2, 03127, Kyiv, Ukraine
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Published Online: 2014-02-15 | DOI: https://doi.org/10.1515/rose-2014-0006

Abstract.

In this paper the heat equation with a random right side is examined. In particular, we give conditions for the existence of solutions in the case when the right side is a random field, sample continuous with probability one from the space Lp(Ω). Estimations for the distribution of the supremum of solutions of such equations are found.

Keywords: Heat equation; stochastic equation

MSC: 35K05; 60G15

About the article

Received: 2013-06-28

Accepted: 2014-01-16

Published Online: 2014-02-15

Published in Print: 2014-03-01


Citation Information: Random Operators and Stochastic Equations, ISSN (Online) 1569-397X, ISSN (Print) 0926-6364, DOI: https://doi.org/10.1515/rose-2014-0006.

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© 2014 by Walter de Gruyter Berlin/Boston. Copyright Clearance Center

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