Evolution Equations Driven by General Stochastic Measures in Hilbert Space

We consider stochastic evolution equations in Hilbert space driven by general stochastic measures. For stochastic measures in the equations we assume $\sigma$-additivity in probability only. The integrals of deterministic functions with respect to stochastic measures in Hilbert space are defined. Ex...

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Bibliographic Details
Published in:Theory of probability and its applications 2015-01, Vol.59 (2), p.328-339
Main Author: Radchenko, V. M.
Format: Article
Language:English
Subjects:
Continuity
Evolution
Hilbert space
Integrals
Mathematical analysis
Stochasticity
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Summary:We consider stochastic evolution equations in Hilbert space driven by general stochastic measures. For stochastic measures in the equations we assume $\sigma$-additivity in probability only. The integrals of deterministic functions with respect to stochastic measures in Hilbert space are defined. Existence and continuity of the mild solutions of the equations are proved.
ISSN:0040-585X
1095-7219
DOI:10.1137/S0040585X97T987119