Generalized Grassmann algebras and applications to stochastic processes

Abstract

In this paper, we present the groundwork for an Itô/Malliavin stochastic cal-culus and Hida's white noise analysis in the context of a supersymmetry withZ3-graded algebras. To this end, we establish a ternary Fock space and the cor-responding strong algebra of stochastic distributions and present its applicationin the study of stochastic processes in this context.