Linear stochastic systems: A white noise approach

Daniel Alpay, David Levanony

Research output: Contribution to journalArticlepeer-review

18 Scopus citations


Using the white noise setting, in particular the Wick product, the Hermite transform, and the Kondratiev space, we present a new approach to study linear stochastic systems, where randomness is also included in the transfer function. We prove BIBO type stability theorems for these systems, both in the discrete and continuous time cases.We also consider the case of dissipative systems for both discrete and continuous time systems.We further study L1-L 2 stability in the discrete time case, and L2-L8 stability in the continuous time case.

Original languageEnglish
Pages (from-to)545-572
Number of pages28
JournalActa Applicandae Mathematicae
Issue number2
StatePublished - 1 Jan 2010


  • Random systems
  • Stability
  • White noise space
  • Wick product

ASJC Scopus subject areas

  • Applied Mathematics


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