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 S ′. As examples, we consider stochastic equations with Wick-type nonlinearity.

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We study the biorthogonal Appell system and Kondrat'ev spaces in the case where the parameter of a ~t-exponential is perturbed by holomorphic invertible functions. The results obtained are applied to the investigation of pseudodifferential equations.Non-Gaussian infinite-dimensional analysis was constructed in [1][2][3] for smooth analytic measures ~t on a dual-kernel space S'. In [4], this was done for a wider class of nondegenerate analytic measures. In the present paper, we generalize some results obtained in [1][2][3][4] to the case of the perturbation of the argument of a p-exponential [2-4] by invertible vector functions holomorphic at zero together with inverse vector functions c~, 15 : Sr ~ Sr (S is the Schwartz space and Sr is its complexification) with the purpose of applying them further to the solution of a certain class of pseudodifferential equations. Consider the rigging S C L2(~) C S', where S is the Schwartz space S = pr limp~ l~-q{p, S" is the dualSchwartz space, S' = ind limp~ ~ H_p, and Hp is a Hilbert space, H_p = Hp (for more details, see, e.g., [5,6]).By (-, .) we denote a canonical pairing between elements of S and S', and I" Ip denotes the norm in Hp.We say that a function G : Sr ~ 9 is holomorphic at zero if there exists a neighborhood of zero U C Sr such that, for all 1"1 ~ U, there exists a neighborhood of zero V such that Ukrainian National Technical University "Kiev Polytechnical Institute."

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