3 citations · 7 across the 23 of their papers we have counts for
21 papers · 1 filter
Distributional comparison for non-commutative infinitely divisible probability measures
Arturo Jaramillo, Josue Vazquez-Becerra
We determine ``cumulant-type'' upper bounds of the non-commutative Wasserstein distance for certain classes of distributions and , which are infinite divisible with respect…
Attenuated Poisson Dirichlet approximations for divisibility configurations
Victor Bernal Ramirez, David Torres-Flores, Arturo Jaramillo
We study the point process formed by the normalized logarithms of the distinct prime factors of a harmonic random sample. We prove a quantitative convergence result, in a Wasserste…
Asymptotics for additive functionals of particle systems via Stein's method
Arturo Jaramillo, Antonio Murillo-Salas
We consider additive functionals of systems of random measures whose initial configuration is given by a Poisson point process, and whose individual components evolve according to…
Non-commutative Stein's Method: Applications to Free Probability and Sums of Non-commutative Variables
Mario Díaz, Arturo Jaramillo
We present a straightforward formulation of Stein's method for the semicircular distribution, specifically designed for the analysis of non-commutative random variables. Our approa…
Approximation of Smooth Numbers for Harmonic Samples A Stein method Approach
Arturo Jaramillo, Xiaochuan Yang
We present a de Bruijn type approximation for quantifying the content of m smooth numbers, derived from samples obtained through a probability measure over the set of integers less…
Rates on Yaglom's limit for Galton-Watson processes in a varying environment
Natalia Cardona-Tobón, Arturo Jaramillo, Sandra Palau
A Galton-Watson process in a varying environment is a discrete time branching process where the offspring distributions vary among generations. It is known that in the critical cas…
Quantitative and stable limits of high-frequency statistics of Lévy processes: a Stein's method approach
Chiara Amorino, Arturo Jaramillo, Mark Podolskij
We establish inequalities for assessing the distance between the distribution of errors of partially observed high-frequency statistics of multidimensional Lévy processes and that…
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…
Optimal estimation of local time and occupation time measure for an α-stable Levy process
Chiara Amorino, Arturo Jaramillo, Mark Podolskij
We present a novel theoretical result on estimation of local time and occupation time measure of an α-stable Lévy process with α in (1, 2). Our approach is based upon computing the…
A generalized Kubilius-Barban-Vinogradov bound for prime multiplicities
Louis H. Y. Chen, Arturo Jaramillo, Xiaochuan Yang
We present an assessment of the distance in total variation of \textit{arbitrary} collection of prime factor multiplicities of a random number in and a collect…
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…
Fluctuations for matrix-valued Gaussian processes
Mario Diaz, Arturo Jaramillo, Juan Carlos Pardo
We consider a symmetric matrix-valued Gaussian process and its empirical spectral measure process . Under some mild condit…
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…
Functional limit theorem for the self-intersection local time of the fractional Brownian motion
Arturo Jaramillo, David Nualart
Let be a -dimensional fractional Brownian motion with Hurst parameter , where . Consider the approximation of the self-intersection local tim…
Asymptotic properties of the derivative of self-intersection local time of fractional Brownian motion
Arturo Jaramillo, David Nualart
Let be a fractional Brownian motion with Hurst parameter . We prove that the approximation of the derivative of self-intersection local time,…
Convergence of the Fourth Moment and Infinite Divisibility: Quantitative estimates
Octavio Arizmendi, Arturo Jaramillo
We give an estimate for the Kolmogorov distance between an infinitely divisible distribution (with mean zero and variance one) and the standard Gaussian distribution in terms of th…
Convergence of the Fourth Moment and Infinite Divisibility
Octavio Arizmendi
In this note we prove that, for infinitely divisible laws, convergence of the fourth moment to 3 is sufficient to ensure convergence in law to the Gaussian distribution. Our result…