Let Φ a locally convex space and Ψ be a quasi-complete, bornological, nuclear space (like spaces of smooth functions and distributions) with dual spaces Φ ′ and Ψ ′ . In this work we introduce sufficient conditions for time regularity properties of the Ψ ′ -valued stochastic convolutionand M is a cylindrical-martingale valued measure on Φ ′ . Our result is latter applied to study time regularity of solutions to Ψ ′ -valued stochastic evolutions equations.
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