Distribution spaces and a new construction of stochastic processes associated with the Grassmann algebra

TL;DR

This paper introduces a new topological algebra of distributions linked to the Grassmann algebra, enabling the analysis of stochastic processes similar to free processes with stationary increments and their derivatives.

Contribution

It presents a novel construction of distribution spaces associated with Grassmann algebra, facilitating the study of related stochastic processes.

Findings

Established a topological algebra of distributions for Grassmann algebra

Enabled analysis of free stochastic processes with stationary increments

Provided tools for studying derivatives of these processes

Abstract

We associate with the Grassmann algebra a topological algebra of distributions, which allows the study of processes analogous to the corresponding free stochastic processes with stationary increments, as well as their derivatives.