Erol Başar, 1938–2017

Tamer Başar , University of Illinois at Urbana - Champaign Editorial Board

New Rates for Exponential Approximation and the Theorems of Rényi and Yaglom1 by Erol

We introduce two abstract theorems that reduce a variety of complex exponential distributional approximation problems to the construction of couplings. These are applied to obtain new rates of convergence with respect to the Wasserstein and Kolmogorov metrics for the theorem of Rényi on random sums and generalizations of it, hitting times for Markov chains, and to obtain a new rate for the clas...

Generalized Gamma Approximation with Rates for Urns, Walks and Trees by Erol

We study a new class of time inhomogeneous Pólya-type urn schemes and give optimal rates of convergence for the distribution of the properly scaled number of balls of a given color to nearly the full class of generalized gamma distributions with integer parameters, a class which includes the Rayleigh, half-normal and gamma distributions. Our main tool is Stein’s method combined with characteriz...

Degree Asymptotics with Rates for Preferential Attachment Random Graphs1 by Erol

We provide optimal rates of convergence to the asymptotic distribution of the (properly scaled) degree of a fixed vertex in two preferential attachment random graph models. Our approach is to show that these distributions are unique fixed points of certain distributional transformations which allows us to obtain rates of convergence using a new variation of Stein’s method. Despite the large lit...

EROL scale: a new behavioural olfactory measure and its relationship with anxiety and depression symptoms.

INTRODUCTION The main objective of this study was to develop and validate a new olfactory measure that assesses the influence of olfaction on several emotional, behavioural, and cognitive issues: The Relational Scale of Olfaction (EROL). A secondary objective was to explore the relationship between the olfactory function and the anxiety and depression symptoms by means of EROL and the Hospital ...