Generalized white noise analysis and topological algebras

Daniel Alpay, Paula Cerejeiras, Uwe Kähler

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper we develop a framework to extend the theory of generalized stochastic processes in the Hida white noise space to more general probability spaces which include the grey noise space. To obtain a Wiener-Itô expansion we recast it as a moment problem and calculate the moments explicitly. We further show the importance of a family of topological algebras called strong algebras in this context. Furthermore we show the applicability of our approach to the study of non-Gaussian stochastic processes.

Original languageEnglish
Pages (from-to)926-958
Number of pages33
JournalStochastics
Volume94
Issue number6
DOIs
StatePublished - 1 Jan 2022
Externally publishedYes

Keywords

  • Non-Gaussian analysis
  • generalized fock space
  • grey noise space
  • strong algebras

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation

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