Banca de DEFESA: DIOGO SOARES DOREA DA SILVA

Uma banca de DEFESA de DOUTORADO foi cadastrada pelo programa.
DISCENTE : DIOGO SOARES DOREA DA SILVA
DATA : 31/07/2020
HORA: 14:00
LOCAL: Online no link http://meet.google.com/mxk-fsfe-bpr
TÍTULO:

The Slow Bond Random Walk and the Snapping Out Brownian Motion

PALAVRAS-CHAVES:

Central Limit Theorem, Slow Bond Random Walk, Snapping Out Brownian Motion.

PÁGINAS: 63
GRANDE ÁREA: Ciências Exatas e da Terra
ÁREA: Probabilidade e Estatística
SUBÁREA: Probabilidade
ESPECIALIDADE: Teoremas de Limite
RESUMO:

We consider the continuous time symmetric random walk with a slow bond on Z, which rates are equal to 1/2 for all bonds, except for the bond of vertices {−1, 0}, which associated rate is given by αn −β /2, where α > 0 and β ∈ [0, ∞] are the parameters of the model. We prove here a functional central limit theorem for the random walk with a slow bond: if β ∈ [0, 1), then it converges to the usual Brownian motion. If β ∈ (1, ∞], then it converges to the reflected Brownian motion. And at the critical value β = 1, it converges to the snapping out Brownian motion (SNOB) of parameter κ = 2α, which is a Brownian type-process recently constructed in 2016 by A. Lejay. 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.

MEMBROS DA BANCA:
Presidente - 1555637 - TERTULIANO FRANCO SANTOS FRANCO
Interno - 2996917 - DIRK ERHARD
Interno - 1518921 - VITOR DOMINGOS MARTINS DE ARAUJO
Externo à Instituição - MARCELO RICHARD HILÁRIO - UFMG
Externo à Instituição - RENATO SOARES DOS SANTOS