Linear State space theory in the white noise space setting
Probability
2009-11-16 v1 Classical Analysis and ODEs
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.
Cite
@article{arxiv.0911.2574,
title = {Linear State space theory in the white noise space setting},
author = {D. Alpay and D. Levanony and A. Pinhas},
journal= {arXiv preprint arXiv:0911.2574},
year = {2009}
}