7 papers
Quantitative limit theorems via relative log-concavity
Arturo Jaramillo, James Melbourne
In this paper we develop tools for studying limit theorems by means of convexity. We establish bounds for the discrepancy in total variation between probability measures and $ν…
Limit Theorems for Additive Functionals of the Fractional Brownian Motion
Arturo Jaramillo, Ivan Nourdin, David Nualart +1
We investigate first and second order fluctuations of additive functionals of a fractional Brownian motion (fBm) of the form \begin{align}\label{eq:abstractmain} Z_n=\left\{\int_{0…
A probabilistic approach to the Erdös-Kac theorem for additive functions
Louis H. Y. Chen, Arturo Jaramillo, Xiaochuan Yang
We present a new perspective of assessing the rates of convergence to the Gaussian and Poisson distributions in the Erdös-Kac theorem for additive arithmetic functions of a ran…
Approximation of Fractional Local Times: Zero Energy and Derivatives
Arturo Jaramillo, Ivan Nourdin, Giovanni Peccati
We consider empirical processes associated with high-frequency observations of a fractional Brownian motion (fBm) with Hurst parameter , and derive conditions under…
Collision of eigenvalues for matrix-valued processes
Arturo Jaramillo, David Nualart
We examine the probability that at least two eigenvalues of an Hermitian matrix-valued Gaussian process, collide. In particular, we determine sharp conditions under which such prob…
Convergence of the empirical spectral distribution of Gaussian matrix-valued processes
Arturo Jaramillo, Juan Carlos Pardo, José Luis Pérez
For a given normalized Gaussian symmetric matrix-valued process , we consider the process of its eigenvalues as well a…