Non-Standard Skorokhod Convergence of Levy-Driven Convolution Integrals in Hilbert Spaces

We study the convergence in probability in the non-standard M-1 Skorokhod topology of the Hilbert valued stochastic convolution integrals of the type to a process driven by a Levy process L. In Banach spaces, we introduce strong, weak. and product modes of -convergence, prove a criterion for the -convergence in probability of stochastically continuous cadlag processes in terms of the convergence in probability of the finite dimensional marginals and a good behavior of the corresponding oscillation functions, and establish criteria for the convergence in probability of Levy driven stochastic convolutions. The theory is applied to the infinitely dimensional integrated Ornstein-Uhlenbeck processes with diagonalizable generators.