6 papers · 1 filter
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…
Symmetric stochastic integrals with respect to a class of self-similar Gaussian processes
Daniel Harnett, Arturo Jaramillo, David Nualart
We study the asymptotic behavior of the -symmetric Riemman sums for functionals of a self-similar centered Gaussian process with increment exponent . We prove that, u…