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 Probability Surveys > Vol. 4 (2007) open journal systems 

A survey of random processes with reinforcement

Robin Pemantle, University of Pennsylvania

The models surveyed include generalized Polya urns, reinforced random walks, interacting urn models, and continuous reinforced processes. Emphasis is on methods and results, with sketches provided of some proofs. Applications are discussed in statistics, biology, economics and a number of other areas.

AMS 2000 subject classifications: Primary 60J20, 60G50; secondary 37A50.

Keywords: urn model, urn scheme, Pólya’s urn, stochastic approximation, dynamical system, exchangeability, Lyapunov function, reinforced random walk, ERRW, VRRW, learning, agent-based model, evolutionary game theory, self-avoiding walk.

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Pemantle, Robin, A survey of random processes with reinforcement, Probability Surveys, 4, (2007), 1-79 (electronic).


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