Abstract
In this paper white noise analysis with respect to the Levy process with negative binomial distributed marginals is investigated. An appropriate space of distributions, E', is used to describe the structure of the Hilbert space of quadratic integrable functionals with respect to the Pascal white noise measure A(NB). The constructed decomposition is used to define a nuclear triple (E)(theta) subset of L-2 (E', A(NB)) subset of (E)(theta)* of test and generalized functions, where theta is a Young function satisfying some suitable conditions. By using the S-transform and the symbol transform sNB, a general characterization theorems are proven for Pascal white noise distributions, white noise test functions and white noise operators in terms of analytical functions with growth condition of exponential type. As application, some quantum stochastic differential equations are solved with special emphasis on Wick calculus.