On regular generalized functions in white noise analysis and their applications (Q2711775)

Regular generalized functions often appear in the theory of stochastic differential equations of the Wick type. Such functions are pointwise defined with respect to the time or space variables being distributions in the variable giving the probability. The authors define and study some spaces of regular generalized functions and, in particular, transforms mapping those spaces to infinite-dimensional versions of Bargmann-Segal and Hardy spaces. Applications to various stochastic equations (the Verhulst equation, the heat equation with a stochastic potential; the viscous Burgers equation with a stochastic source; the Wick type Burgers equation) are given.