Generalized Grassmann algebras and applications to stochastic processes

Abstract

In this paper we present the groundwork for an Itô/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.

References in corpus (7)

• Introduction to Supersymmetric Theory of Stochastics
• Self-Organized Criticality as Witten-type Topological Field Theory with Spontaneously Broken Becchi-Rouet-Stora-Tyutin Symmetry
• Distributions and Integration in superspace
• Distribution spaces and a new construction of stochastic processes associated with the Grassmann algebra
• Positivity, rational Schur functions, Blaschke factors, and other related results in the Grassmann algebra
• Pizzetti and Cauchy formulae for higher dimensional surfaces: a distributional approach
• Generalized Fock space and moments