Flows in near algebras with applications to harnesses

TL;DR

This paper introduces new flow concepts in near algebras, providing parametric representations and applications to probabilistic processes like harnesses and quadratic harnesses, extending previous results.

Contribution

It develops the theory of one-way and two-way flows in near algebras with explicit flow generator representations and applies these to probabilistic structures such as harnesses.

Findings

Parametric representations of flows in near algebras.

Application to polynomial stochastic processes.

Generalization of existing results on harnesses.

Abstract

We introduce one-way flows in near algebras and two-way flows in double near algebras with two interrelated multiplications. We establish parametric representations of the one-way and two-way flows in terms of a single element of the algebra that we call a flow generator. We indicate probabilistic applications of the one-way flows to a study of polynomial stochastic processes. We apply our results on the two-way flows to harnesses and quadratic harnesses in probability theory, generalizing some previous results.