Abstract
We consider stochastic chains on abstract measurable spaces whose evolution at any given time depends on the present position and on the occupation measure created by the path up to this instant. This generalization of reinforced random walks enables us to impose conditions ensuring L p , p⩾1, or a.s. convergence of the empirical measures towards some fixed point of a probability–valued dynamical system. We present two sets of hypotheses based on weak contraction properties, leading to two different proofs, but in both situations the rates of convergence are optimal in the examined level of generality.
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Schedule a callMore From: Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
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