Limits of random iterates
Copyright policy )Limits of random iterates
Summary: Given a probability space \((\Omega, {\mathcal A},P)\), a nonempty subset \(X\) of a separable Banach space \(Y\) and an random-valued function \(f: X\times\Omega\to X\), we assume that the sequence of iterates of \(f\) converges to a function \(\xi: X\times\Omega^{\infty}\to Y\). We give conditions on \(f\) and types of convergence which imply continuity of \(\xi\) with respect to the first variable. A possible application of obtained results to iterative equations is presented.
converges, Banach space, iterative equations, Functional equations for functions with more general domains and/or ranges, Random-valued vector functions, sequences of iterates, continuous solutions, Iteration theory, iterative and composite equations, probability space
converges, Banach space, iterative equations, Functional equations for functions with more general domains and/or ranges, Random-valued vector functions, sequences of iterates, continuous solutions, Iteration theory, iterative and composite equations, probability space
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