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A stopped Doob inequality for stochastic convolution integrals and stochastic evolution equations. (English) Zbl 0552.60058
A stopped Doob inequality is proved for stochastic convolution integrals of the type \(\int_{(0,t]}U(t,s^-)\Phi (s)dM(s)\) where M is a square integrable Hilbert space-valued cadlag martingale, \(\Phi\) an operator valued predictable function and U a contraction evolution operator. This is then used to obtain the existence of a mild solution for a wider class of nonlinear stochastic evolution equations with memory.
Reviewer: R.Curtain

MSC:
60H20 Stochastic integral equations
60G44 Martingales with continuous parameter
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