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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.


This is a pre-copy-editing, author-produced PDF of an article accepted for publication in SIAM Journal on Control and Optimization (SICON), volume 48, issue 8, in 2010 following peer review. The definitive publisher-authenticated version is available online at DOI: 10.1137/090777116

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Society for Industrial and Applied Mathematics



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