Seminario de Probabilidad y Estadística
Título: "The Slow Bond Random Walk and the Snapping Out Brownian Motion."
Expositor: Trtuliano Franco (Universidade Federal da Bahia, Brasil)
Resumen:
We consider a continuous time symmetric random walk on the integers, whose rates are equal to 1/2 for all bonds, except for the bond of vertices {−1, 0}, which associated rate is given by \alpha n^{-\beta}/2 , where \alpha and \beta are parameters of the model. We prove here a functional central limit theorem for the random walk with a slow bond: if \beta<1, then it con verges to the usual Brownian motion. If \beta>1, then it converges to the reflected Brownian motion. And at the critical value \beta = 1, it converges to the snapping out Brownian motion (SNOB) of parameter k = 2 \alpha, which is a Brow nian type- process recently constructed by Lejay (2016). We also provide Berry-Esseen estimates in the dual bounded Lipschitz metric for the weak convergence of one-dimensional distributions, which we believe to be sharp. Talk based on a joint work with D. Erhard and D. Silva.
Viernes 10/9 a las 10:30, zoom
Contacto: Alejandro Cholaquidis - acholaquidis@hotmail.com
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