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SUMMARY:Perturbed random walks and a skew Brownian motion (Lecture 2) - An
 drey Pilipenko (National Academy of Sciences of Ukraine)
DTSTART:20240801T090000Z
DTEND:20240801T100000Z
UID:TALK218701@talks.cam.ac.uk
DESCRIPTION:In this lecture we study the Donsker scaling limit of integer-
 valued random walks perturbed on a finite subset of Z called a membrane. U
 nder very mild assumptions about the law of the random walk&rsquo\;s incre
 ments inside and outside of the membrane we show weak convergence of the s
 caled processes to a skew Brownian motion and give the explicit formula fo
 r its permeability parameter in terms of stationary distributions of certa
 in embedded Markov chains. The proof is based on a representation of the o
 riginal random walk as a multidimensional coordinate process and its conve
 rgence to a Walsh Brownian motion.
LOCATION:Seminar Room 2\, Newton Institute
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