Generalized Grassmann algebras and applications to stochastic processes

Daniel Alpay, Paula Cerejeiras, Uwe Kähler

Published 2021-03-21Version 1

In this paper we present the groundwork for an It\^o/Malliavin stochastic calculus and Hida's white noise analysis in the context of a supersymmentry with Z3-graded algebras. To this end we establish a ternary Fock space and the corresponding strong algebra of stochastic distributions and present its application in the study of stochastic processes in this context.