Time regularity of stochastic convolutions and stochastic evolution equations in duals of nuclear spaces

Abstract

Let be a locally convex space and let be a quasi-complete bornological nuclear space (like spaces of smooth functions and distributions) with dual spaces and In this work we introduce sufficient conditions for time regularity properties of the -valued stochastic convolution where is the dual semigroup to a C 0-semigroup on is a suitable operator form into and M is a cylindrical-martingale valued measure on Our result is latter applied to study time regularity of solutions to -valued stochastic evolutions equations.