Banca de DEFESA: JOSE CRISANTO DA COSTA NETO

Uma banca de DEFESA de DOUTORADO foi cadastrada pelo programa.
DISCENTE : JOSE CRISANTO DA COSTA NETO
DATA : 17/08/2018
HORA: 10:00
LOCAL: AUDITÓRIO DO DFTE
TÍTULO:

Formal power series for the stable distributions of Lévy: the symmetric case.

PALAVRAS-CHAVES:

Stable Distributions, Central Theorem Limit, Hypergeometric Series, Divergent Series, Regularization, Summability, Approach in Series.

PÁGINAS: 105
GRANDE ÁREA: Ciências Exatas e da Terra
ÁREA: Física
SUBÁREA: Física da Matéria Condensada
RESUMO:

A relevant problem in Statistical Physics and Mathematical Physics is to derive numerically precise expressions and exact analytical forms to calculate the distributions of Lévy α-stable P_α(x;β). In practice, these distributions are usually expressed in terms of the Fourier Integral of its characteristic function. In fact, known closed-form expressions are relatively scarce given the huge space of parameters: 0 < α ≤ 2 (Lévy index), -1 ≤ β ≤ 1 (asymmetry), σ > 0 (scale) and - ∞ < µ < ∞ (offset). In the formal context, important exact results rely on special functions,

such as the Meijer-G, Fox-H functions and finite sum of hypergeometric functions, with only a few exceptional cases expressed

in terms of elementary functions (Gaussian and Cauchy distributions). From a more practical point of view, methods such as series expansions, e.g., allow an estimation of the Lévy distributions with high numerical precision, but most of the approaches are restricted to a small subset of the parameters and, although sophisticated, this algorithms are time-consuming. As an additional contribution to this problem, we propose new methods to describe the symmetric stable distributions, with parameters β = 0, µ = 0, σ = 1. We obtain a description through a closed analytical form, via series of formal power making use of the Borel regularization sum procedure (for α = 2/M, M = 1, 2, 3...). Furthermore we obtain an approximate expression (for 0 < α ≤ 2) by dividing the domain of the integration variable into sub-intervals (windows), performing proper series expansion

inside each window, and then calculating the integrals term by term.

MEMBROS DA BANCA:
Interno - 1519258 - DORY HELIO AIRES DE LIMA ANSELMO
Externo à Instituição - ERNESTO CARNEIRO PESSOA RAPOSO - UFPE
Interno - 2492756 - JOAO MEDEIROS DE ARAUJO
Presidente - 1294916 - MADRAS VISWANATHAN GANDHI MOHAN
Externo à Instituição - MARCOS GOMES ELEUTERIO DA LUZ - UFPR