Generalized Grassmann algebras and applications to stochastic processes. (20th September 2021)

• Record Type: Journal Article
• Authors: Alpay, Daniel; Cerejeiras, Paula; Kaehler, Uwe
• Is Part Of: Mathematical methods in the applied sciences. Volume 45:Number 1(2022)
• Page Start: 383
• Page End: 401
• Publication Date: 2021-09-20
• Subjects: Fock space -- hypersymmetry -- stochastic process -- ternary Grassmann algebra; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.7781
• Languages: English
• ISSNs: 0170-4214

Abstract

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 supersymmetry with ℤ 3 ‐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.