Linear stochastic systems: Awhite noise approach

Daniel Alpay; David Levanony

doi:10.1007/s10440-009-9461-1

Linear stochastic systems: Awhite noise approach

Daniel Alpay, David Levanony

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

18 Scopus citations

Abstract

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 language	English
Pages (from-to)	545-572
Number of pages	28
Journal	Acta Applicandae Mathematicae
Volume	110
Issue number	2
DOIs	https://doi.org/10.1007/s10440-009-9461-1
State	Published - 1 Jan 2010

Keywords

Random systems
Stability
White noise space
Wick product

ASJC Scopus subject areas

Applied Mathematics

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AU - Levanony, David

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AB - 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.

KW - Random systems

KW - Stability

KW - White noise space

KW - Wick product

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IS - 2

ER -

Linear stochastic systems: Awhite noise approach

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Keywords

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