Properties of integrals with respect to a general stochastic measure in a stochastic heat equation. (English. Ukrainian original) Zbl 1232.60043

Radchenko, V. M.

Theory Probab. Math. Stat. 82, 103-114 (2011); translation from Teor. Jmovirn. Mat. Stat. No. 82, 104-114.

Summary: 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.

MSC:

60H05	Stochastic integrals
60H15	Stochastic partial differential equations (aspects of stochastic analysis)

References:

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