Tesko V. A.
Ukr. Mat. Zh. - 2009. - 61, № 6. - pp. 733-764
We review some recent results related to stochastic integrals of the Hitsuda–Skorokhod type acting on the extended Fock space and its riggings.
Ukr. Mat. Zh. - 2007. - 59, № 5. - pp. 588–617
We propose a generalization of an extended stochastic integral to the case of integration with respect to a broad class of random processes. In particular, we obtain conditions for the coincidence of the considered integral with the classical Itô stochastic integral.
Orthogonal Approach to the Construction of the Theory of Generalized Functions of Infinitely Many Variables and the Poisson Analysis of White Noise
Ukr. Mat. Zh. - 2004. - 56, № 12. - pp. 1587-1615
We develop an orthogonal approach to the construction of the theory of generalized functions of infinitely many variables (without using Jacobi fields) and apply it to the construction and investigation of the Poisson analysis of white noise.
Spaces appearing in the construction of infinite-dimensional analysis according to the biorthogonal scheme
Ukr. Mat. Zh. - 2004. - 56, № 7. - pp. 977–990
We study properties of annihilation operators of infinite order that act in spaces of test functions. The results obtained are used for establishing the coincidence of spaces of test functions.
Ukr. Mat. Zh. - 2003. - 55, № 12. - pp. 1587-1657
We present main recent results on the generalization of white-noise analysis related to a family of generalized translation operators.