Generalized Grassmann algebras and applications to stochastic processes

Daniel Alpay; Paula Cerejeiras; Uwe Kaehler

doi:10.1002/mma.7781

Generalized Grassmann algebras and applications to stochastic processes

Daniel Alpay, Paula Cerejeiras, Uwe Kaehler

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

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 (Formula presented.) -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.

Original language	English
Pages (from-to)	383-401
Number of pages	19
Journal	Mathematical Methods in the Applied Sciences
Volume	45
Issue number	1
DOIs	https://doi.org/10.1002/mma.7781
State	Published - 15 Jan 2022
Externally published	Yes

Keywords

Fock space
hypersymmetry
stochastic process
ternary Grassmann algebra

ASJC Scopus subject areas

General Mathematics
General Engineering

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10.1002/mma.7781

Cite this

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AB - 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 (Formula presented.) -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.

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KW - stochastic process

KW - ternary Grassmann algebra

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Generalized Grassmann algebras and applications to stochastic processes

Abstract

Keywords

ASJC Scopus subject areas

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