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Linear Stochastic Systems: A White Noise Approach

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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 ℓ 1-ℓ 2 stability in the discrete time case, and L 2-L ∞ stability in the continuous time case.

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Authors and Affiliations

  1. Department of Mathematics, Ben-Gurion University of the Negev, P.O. Box 653, Beer-Sheva, 84105, Israel

    Daniel Alpay

  2. Department of Electrical Engineering, Ben-Gurion University of the Negev, P.O. Box 653, Beer-Sheva, 84105, Israel

    David Levanony

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  1. Daniel Alpay
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Alpay, D., Levanony, D. Linear Stochastic Systems: A White Noise Approach. Acta Appl Math 110, 545–572 (2010). https://doi.org/10.1007/s10440-009-9461-1

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