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University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Perturbed random walks and a skew Brownian motion (Lecture 2)

## Perturbed random walks and a skew Brownian motion (Lecture 2)Add to your list(s) Download to your calendar using vCal - Andrey Pilipenko (National Academy of Sciences of Ukraine)
- Thursday 01 August 2024, 10:00-11:00
- Seminar Room 2, Newton Institute.
If you have a question about this talk, please contact nobody. 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. ## This talk is included in these lists:- All CMS events
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