Kachanovskyy M. Elements of non-Gaussian analysis on spaces of functions of infinite-many variables

The dissertation is devoted to construction of elements of a non-Gaussian infinite-dimensional analysis using the biorthogonal approach, and to construction of elements of the white noise analysis that is connected with the so-called generalized Meixner measure. Properties of the test functions spaces and some operators on these spaces are studied. Elements of the Wick calculus on the generalized functions spaces are constructed. Analogs of the extended stochastic integral, stochastic derivatives and operators of stochastic differentiation on the spaces of test and generalized functions are constructed and studied. Taking into account the specificity of orthogonal decomposition for the space of square integrable with respect to the generalized Meixner measure functions, we construct and study the extended stochastic integral, the stochastic derivatives and the operators of stochastic differentiation on this space and on its rigging by the parametrized spaces of test and regular generalized functions. The integration by parts formula is obtained. Elements of the Wick calculus on the parametrized spaces of regular generalized functions are constructed. Some elements of stochastic calculus are transferred to the extended Fock space and its riggings, the obtained by this transfer results are used in order to construct elements of the coloured noise analysis.