Extended Stochastic Integral and Wick Calculus on Spaces of Regular Generalized Functions Connected with Gamma Measure

We introduce and study an extended stochastic integral, a Wick product, and Wick versions of holomorphic functions on Kondrat'ev-type spaces of regular generalized functions. These spaces are connected with the Gamma measure on a certain generalization of the Schwartz distribution space . As examples, we consider stochastic equations with Wick-type nonlinearity. This paper is dedicated to Professor Yu. M. Berezansky, who is one of my mentors __________ Published in Ukrains'kyi Matematychnyi Zhurnal, Vol. 57, No. 8, pp. 1030–1057, August, 2005.