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Nonlocal Cauchy problem for second order stochastic evolution equations in Hilbert spaces. (English) Zbl 1151.34046

The authors study the existence of mild solutions of second-order stochastic evolution equations with non-local conditions in Hilbert space. Their methods avoid the cosine and sine family of operators often used, but allow the introduction of noise into concrete models. There is a useful introductory section on earlier work.

MSC:

34F05 Ordinary differential equations and systems with randomness
34G20 Nonlinear differential equations in abstract spaces
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
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