A combinatorial construction of the multiple stochastic integral is developed using sequences in Clifford (geometric) algebras. In particular, sequences of Berezin integrals in an ascending chain of geometric algebras converge in mean to the iterated stochastic integral. By embedding such chains within an infinite-dimensional Clifford algebra, an infinitedimensional analogue of the Berezin inte...

Abstract It has been known for over 70 years that there is an asymptotic transition of Charlier polynomials to Hermite polynomials. This transition, which still presented in its classical form modern reference works, valid if and only a certain parameter integer. In this light, it surprising much more powerful exists from the function , any real value parameter. greatly strengthens connections ...

The paper presents a new approach to the computational treatment of polyreaction kinetics. This approach is characterized by a Galerkin method based on orthogonal polynomials of a discrete variable, the polymer degree (or chain length). In comparison with the known competing approaches (statistical moment treatment, Galerkin methods for continuous polymer models), the suggested method is shown ...

We introduce the concept of D-operators associated to a sequence of polynomials (pn)n and an algebra A of operators acting in the linear space of polynomials. In this paper, we show that this concept is a powerful tool to generate families of orthogonal polynomials which are eigenfunctions of a higher order difference or differential operator. Indeed, given a classical discrete family (pn)n of ...

For any sequence of polynomials {pk(t)} in one real or complex variable, where pk has degree k for k≥0, we find explicit expressions and recurrence relations infinite matrices whose entries are the numbers d(n,m,k), called linearization coefficients, that satisfypn(t)pm(t)=∑k=0n+md(n,m,k)pk(t),n,m≥0. pair polynomial sequences {uk(t)} e(n,m,k) satisfypn(t)pm(t)=∑k=0n+me(n,m,k)uk(t),n,m≥0. We als...