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On stochastic modelling for discrete bilinear systems in Hilbert space

✍ Scribed by C.S. Kubrusly

Publisher
Elsevier Science
Year
1989
Tongue
English
Weight
829 KB
Volume
31
Category
Article
ISSN
0378-4754

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✦ Synopsis

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.

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## Abstract The cornerstone of the theory of discrete‐space single‐input–single‐output linear systems is the idea that every such system has an input–output map that can be represented by a convolution or the familiar generalization of a convolution. This thinking involves an oversight which, for t