Volodymyr Tesko

Universidade Federal do ABC (UFABC) | UFABC · Centro de Matemática Computação e Cognição (CMCC)

We investigate the H-stochastic integral introduced in [24]. It is known that this integral generalizes the classical It^o stochastic integral and the It^o integral on a Fock space. In the present paper we construct and study an extension of the H-stochastic integral which will generalize the Hitsuda{Skorokhod integral.

Let $\ast_P$ be a product on $l_{\rm{fin}}$ (a space of all finite sequences) associated with a fixed family $(P_n)_{n=0}^{\infty}$ of real polynomials on $\mathbb{R}$. In this article, using methods from the theory of generalized eigenvector expansion, we investigate moment-type properties of $\ast_P$-positive functionals on $l_{\rm{fin}}$. If $(P...

In this paper we construct and study an integral of operator-valued functions with respect to Hilbert space-valued measures generated by a resolution of identity. Our integral generalizes the Itô stochastic integral with respect to normal martingales and the Itô integral on a Fock space. In this paper we construct and study an integral of operator...

We review some recent results related to stochastic integrals of the Hitsuda–Skorokhod type acting on the extended Fock space and its riggings.

In this article, we review some recent developments in white noise analysis and its generalizations. In particular, we describe the main idea of the biorthogonal approach to a generalization of white noise analysis, connected with the theory of hypergroups.

In this note we define and study a Hilbert space-valued stochastic integral of operator-valued functions with respect to Hilbert space-valued measures. We show that this integral generalizes the classical Itô stochastic integral of adapted processes with respect to normal martingales and the Itô integral in a Fock space.

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.

We reconstruct a family of generalized translation operators from the function which generates a given theory of generalization function.

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.

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.

We present main recent results on the generalization of white-noise analysis related to a family of generalized translation operators.