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Evolution equations driven by general stochastic measures in Hilbert space. (English. Russian original) Zbl 1315.60004

Theory Probab. Appl. 59, No. 2, 328-339 (2015); translation from Teor. Veroyatn. Primen. 59, No. 2, 375-386 (2014).
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.

MSC:

60B11 Probability theory on linear topological spaces
60H05 Stochastic integrals
47D06 One-parameter semigroups and linear evolution equations
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