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| The objective of this talk is the introduction of cylindrical L{\'e}vy processes and their stochastic integrals in Hilbert spaces.
The degree of freedom of models in infinite dimensions is often reflected by the request that each mode along a dimension is independently perturbed by the noise. In the Gaussian setting, this leads to the {\em cylindrical Wiener process } including from a model point of view the very important possibility to model a Gaussian noise in both time and space in a great flexibility (space-time white noise). Up to very recently, there has been no analogue for L{\'e}vy processes.
Based on the classical theory of cylindrical processes and cylindrical measures we introduce {\em cylindrical L{\'e}vy processes} as a natural generalisation of cylindrical Wiener processes. In Hilbert spaces we introduce a stochastic integral for operator-valued stochastic processes with respect to cylindrical L{\'e}vy processes. |
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