Abstract
It is shown that every stochastic automaton generates a semigroup of continuous linear operators in order to give conditions for the convergence of certain operators connected with infinite input sequences. The main results of this note are conditions for the infinitesimal stability of stochastic automata. Since under suitable conditions the behaviour of a learning system can be represented by a stochastic automaton, these results apply to the asymptotic stability of learning.
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Doberkat, EE. Convergence theorems for stochastic automata and learning systems. Math. Systems Theory 12, 347–359 (1978). https://doi.org/10.1007/BF01776582
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DOI: https://doi.org/10.1007/BF01776582