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Perturbed random walks and a skew Brownian motion (Lecture 2)

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SSD - Stochastic systems for anomalous diffusion

In this lecture we study the Donsker scaling limit of integer-valued random walks perturbed on a finite subset of Z called a membrane. Under very mild assumptions about the law of the random walk’s increments inside and outside of the membrane we show weak convergence of the scaled processes to a skew Brownian motion and give the explicit formula for its permeability parameter in terms of stationary distributions of certain embedded Markov chains. The proof is based on a representation of the original random walk as a multidimensional coordinate process and its convergence to a Walsh Brownian motion.

This talk is part of the Isaac Newton Institute Seminar Series series.

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