On stochastic modelling for discrete bilinear systems in Hilbert space

Abstract

Infinite-dimensional discrete-time bilinear models driven by Hilbert-space-valued random sequences can be rigorously defined as the uniform limit of finite-dimensional bilinear models. Existence and uniqueness of solutions for such infinite-dimensional models can be established by assuming only independence and structural similarity for the stochastic environment under consideration. Uniform structure equiconvergence implies uniform state convergence under suitable stability-like conditions.