On the absolute global convergence of fliess operators driven by L2-Itô processes

Fliess operators have been an object of study in connection with nonlinear systems acting on deterministic inputs since the early 1970's. They describe a broad class of nonlinear input-output maps using a type of functional series expansion. But in most applications, a system's inputs have noise components. It has been shown that the notion of a Fliess operator can be generalized to admit a class of L2-Ito¿ stochastic input processes, and that they converge conditionally over an arbitrarily large but finite interval of time. The purpose of this paper is to prove the more difficult proposition that Fliess operators driven by L2-Ito¿ stochastic processes converge absolutely under the same conditions.