Stochastic Partial Differential Equations with non Gaussian White Noise and Corresponding Generators

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The project is aimed at the investigation of a number of recent important problems in (infinite dimensional) stochastic analysis related to the study of non Gaussian driven stochastic partial differential equations (SPDEs) on the basis of a unified analysis on Poisson spaces and Wiener spaces. This study shall also involve Dirichlet forms in infinite dimensional settings and applications to the construction of nontrivial models in quantum field theory (QFT). Particular attention will be given to the analysis of various Poisson type spaces (including the multiparameter case, i.e., Poisson fields) and jump type processes (or random fields) in infinite dimensional state spaces, as basic tools for the construction of infinite dimensional stochastic systems.