Linear State space theory in the white noise space setting

2009/11/13 by Daniel Alpay, D. Alpay, Alpay, D. +6
Mathematics · Physics and Astronomy · #46E22 #47B32 #60H40 #93E03 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Holomorphic and Operator Theory #Probability (math.PR) #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics #math.CA #math.PR #msc:46E22 #msc:47B32 #msc:60H40 #msc:93E03

paper · pdf · doi:10.48550/arxiv.0911.2574

arxiv created 2009/11/13 · openalex publication_date 2009/11/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study state space equations within the white noise space setting. A commutative ring of power series in a countable number of variables plays an important role. Transfer functions are rational functions with coefficients in this commutative ring, and are characterized in a number of ways. A major feature in our approach is the observation that key characteristics of a linear, time invariant, stochastic system are determined by the corresponding characteristics associated with the deterministic part of the system, namely its average behavior.

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