Banca de DEFESA: ÉRIC CARVALHO ROCHA

Uma banca de DEFESA de DOUTORADO foi cadastrada pelo programa.
STUDENT : ÉRIC CARVALHO ROCHA
DATE: 23/09/2020
TIME: 15:00
LOCAL: Plataforma Google Meet
TITLE:

Complex analytical structure of stable Lévy distributions

KEY WORDS:

Lévy Stable Distribution, Random Walks, Stochastic Processes.

PAGES: 92
BIG AREA: Ciências Exatas e da Terra
AREA: Física
SUMMARY:

The almost ubiquitous Lévy α-stable distributions lack general closed-form expressions in terms of elementary functions—Gaussian and Cauchy cases being notable exceptions. To better understand this 80-year-old conundrum, we study the complex analytic continuation p_α (z), z ∈ C , of the Lévy α-stable distribution family p_α (x), x ∈ R, parametrized by 0 < α ≤ 2. We first extend known but intricate results, and give a new proof that p_α (z) is holomorphic on the entire complex plane for 0 < α ≤ 2, whereas p_α (z) is not even meromorphic on C for 0 < α < 1. Next, we unveil the complete complex analytic structure of p_α (z) using domain coloring. Finally, motivated by these insights, we argue, that possibly, there cannot be closed-form expressions in terms of elementary functions for p_α (x) for general α.

BANKING MEMBERS:
Interno - 1519258 - DORY HELIO AIRES DE LIMA ANSELMO
Externo à Instituição - ERNESTO CARNEIRO PESSOA RAPOSO - UFPE
Interno - 6346140 - LUCIANO RODRIGUES DA SILVA
Presidente - 1294916 - MADRAS VISWANATHAN GANDHI MOHAN
Externo à Instituição - MARCOS GOMES ELEUTERIO DA LUZ - UFPR