| Contents |
| In many problems of engineering, physics or finance, the evolution of a stochastic system
can be described by stochastic convolution integrals of a deterministic kernel with respect to a L{\'e}vy process in a Hilbert space. In this talk we study the convergence in probability of a stochastic convolution integral process for kernels depending on a parameter.
For many examples, the appropriate topology is not the standard but another Skorokhod topology ($M_1$), which is much less often studied. It turns out that in infinite dimensional Hilbert spaces there are three different kinds of this non-standard Skorokhod topology, i.e in a strong, weak and product sense. We establish a general characterisation for a sequence of stochastic processes in a Hilbert space to converge in these non-standard Skorokhod topologies in terms of a corresponding oscillation function. The results are applied to the infinite dimensional integrated Ornstein-Uhlenbeck process with a diagonalisable generator. |
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