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Explore a mathematical lecture from Professor Andrey Pilipenko of the National Academy of Sciences of Ukraine examining the Donsker scaling limit of integer-valued random walks perturbed on a finite subset of Z. Delve into the weak convergence of scaled processes to a skew Brownian motion, with detailed explanations of the permeability parameter's formula derived from stationary distributions of embedded Markov chains. Learn how the proof methodology utilizes a representation of the original random walk as a multidimensional coordinate process and its convergence to a Walsh Brownian motion. Part of the Stochastic Systems for Anomalous Diffusion seminar series at the Isaac Newton Institute, this advanced mathematics presentation provides rigorous insights into perturbed random walks and their relationship to skew Brownian motion theory.
