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Theory of Probability and Mathematical Statistics

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Properties of integrals with respect to a general stochastic measure in a stochastic heat equation


Author: V. M. Radchenko
Translated by: Oleg Klesov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 82 (2010).
Journal: Theor. Probability and Math. Statist. 82 (2011), 103-114
MSC (2010): Primary 60G57, 60H15, 60H05
DOI: https://doi.org/10.1090/S0094-9000-2011-00830-7
Published electronically: August 4, 2011
MathSciNet review: 2790486
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Abstract | References | Similar Articles | Additional Information

Abstract: We prove a theorem on the continuity with respect to a parameter and an analogue of Fubini's theorem for integrals with respect to a general stochastic measure defined on Borel subsets of  $ \mathbb{R}$. These results are applied to study the stochastic heat equation considered in a mild as well as in a weak form.


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Additional Information

V. M. Radchenko
Affiliation: Department of Mathematical Analysis, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue 2, Kiev 03127, Ukraine
Email: vradchenko@univ.kiev.ua

DOI: https://doi.org/10.1090/S0094-9000-2011-00830-7
Keywords: Random measure, stochastic integral, stochastic Fubini theorem, stochastic convolution
Received by editor(s): October 5, 2009
Published electronically: August 4, 2011
Additional Notes: The research is supported by the Swedish Institute, grant SI-01424/2007
Article copyright: © Copyright 2011 American Mathematical Society

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