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

Radchenko, V.

doi:10.1090/S0094-9000-2011-00830-7

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

Author: V. M. Radchenko
Translated by: Oleg Klesov
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: 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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