13 citations · 60 across the 82 of their papers we have counts for
27 papers · 1 filter
Independence of the indicator functions of record values for Multivariate independent data
Gane Samb Lo, El Hadji Babou
We consider a sequence of random vectors on \(\mathbb{R}^d, \ d\geq 1\). We consider the record values based on the simultaneous strict inequality of the coordinates. The indicator…
Elements of Randoms Analysis about the Gamma Generalized Hyperbolic Distribution Levy Stochastic Process
Nafy Ngom, Aladji Babacar Niang, Soumaila Dembele +1
In this paper, we study some aspects on random analysis on the Léevy stochastic processes with margins following generalized hyperbolic distributions generated by gamma laws. In pa…
The exact probability law for the approximated similarity from the Minhashing method
Soumaila Dembele, Gane Samb Lo
We propose a probabilistic setting in which we study the probability law of the Rajaraman and Ullman \textit{RU} algorithm and a modified version of it denoted by \textit{RUM}. The…
-Central limit theorems and -invariance principles for associated random variables
Aladji Babacar Niang, Akym Adekpedjou, Harouna Sangaré +1
The investigation asymptotic limits on associated data mainly focused on limit theorems of summands of associated data and on the related invariance principles. In a series of pape…
Poisson invariance principles from two classical Poisson limit theorems and extension to non-stationary independent sequences
Aladji Babacar Niang, Gane Samb Lo, Chérif Mamadou Moctar Traoré +1
The simple Lévy Poisson process and scaled forms are explicitly constructed from partial sums of independent and identically distributed random variables and from sums of non-stati…
Extensions of two classical Poisson limit laws to non-stationary independent data
Aladji Babacar Niang, Harouna Sangaré, Tchilabalo Abozou Kpanzou +2
In earlier stages in the introduction to asymptotic methods in probability theory, the weak convergence of sequences of Binomial of random variables (\textit{rv}'…
Simultaneous Joint Lower and Upper record values Probability Laws for Absolutely Continuous or Discrete Data
Gane Samb Lo, Mohammad Ahsanullah, Aladji Babacar Niang
This paper investigates the probability density function () of the -vector of both lower and upper record values for a sequence of independent random varia…
Central limit theorems for associated possibly moving partial sums and application to the non-stationary invariance principle
Akim Adekpedjou, Aladji Babacar Niang, Chérif Mamadou Moctar Traoré +1
General Central limit theorem deals with weak limits (in type) of sums of row-elements of array random variables. In some situations as in the invariance principle problem, the sum…
Asymptotics of summands I: square integrable independent random variables
Aladji Babacar Niang, Gane Samb Lo, Moumouni Diallo
This paper is part of series on self-contained papers in which a large part, if not the full extent, of the asymptotic limit theory of summands of independent random variables is e…
A detailed and direct proof of Skorohod-Wichura's theorem
Gane Samb Lo, Aladji Babacar Niang, Lois Chinwendu Okereke
The representation Skorohod theorem of weak convergence of random variables on a metric space goes back to Skorohod (1956) in the case where the metric space is the class of real-v…
An introduction to a general records theory both for dependent data and high dimensions: revisited 2
Gane Samb Lo, Mohammad Ahsanullah
The probabilistic investigation on record values and record times of a sequence of random variables defined on the same probability space has received much attention from 1952 to n…
Finiteness of Record values and Alternative Asymptotic Theory of Records with Atom Endpoints
Gane Samb Lo, Harouna Sangaré, Mamadou Cherif Traoré +1
Asymptotic theories on record values and times, including central limit theorems, make sense only if the sequence of records values (and of record times) is infinite. If not, such…
Asymptotic laws for upper and strong record values in the extreme domain of attraction and beyond
Gane Samb Lo, Mohammad ahsanullah
Asymptotic laws of records values have usually been investigated as limits in type. In this paper, we use functional representations of the tail of cumulative distribution function…
Weak Convergence (IIA) - Functional and Random Aspects of the Univariate Extreme Value Theory
Gane Samb Lo, Modou Ngom, Tchilabola Abozou Kpanzou +1
The univariate extreme value theory deals with the convergence in type of powers of elements of sequences of cumulative distribution functions on the real line when the power index…
Mathematical Foundations of Probability Theory
Gane Samb Lo
In the footsteps of the book \textit{Measure Theory and Integration By and For the Learner} of our series in Probability Theory and Statistics, we intended to devote a special volu…
A simple proof of the theorem of Sklar and its extension to distribution functions
Gane Samb Lo
In this note we provide a quick proof of the Sklar's Theorem on the existence of copulas by using the generalized inverse functions as in the one dimensional case, but a little mor…
General Central Limit Theorems for Associated Sequences
Harouna Sangaré, Gane Samb Lo
In this paper, we provide general central limit theorems (CLT's) for associated random variables (rv's) following the approaches used by Newman (1980) and Olivera et al.(2012). Giv…
Invariance principles for random sums of random variables
Gane Samb Lo
This note investigates invariance principles for sums of N(nt) iid radom variables, where n is an integer, t is a positive real number and N(u) is a stochastic process with nonnega…
Weak Convergence (IA). Sequences of Random Vectors
Gane Samb Lo, Modou Ngom, Tchilabalo Atozou Kpanzou
(English) This monograph aims at presenting the core weak convergence theory for sequences of random vectors with values in . In some places, a more general formulati…
A general strong law of large numbers and applications to associated sequences and to extreme value theory
Harouna Sangare, Gane Samb Lo
The purpose of this paper is to establish a general strong law of large numbers (SLLN) for arbitrary sequences of random variables (rv's) based on the squared indice method and to…
Another look at Second order condition in Extreme Value Theory
Gane Samb Lo, Adja Mbarka Fall
This note compares two approaches both alternatively used when establishing normality theorems in univariate Extreme Value Theory. When the underlying distribution function ()…
A note on a new exponential bound for M-acceptable random variables
Gane Samb Lo, Cheikhna Hamallah Ndiaye
We present a new exponential inequality as a generalization of that of Sung \textit{et al.} \cite{sun2011} for -acceptable random variables, and hence for extended negative ones…
A remark on the asymptotic tightness in
Gane Samb Lo
In this note, we extend a simple criteria for uniform tightness in , the class of real continuous functions defined on , given in Theorem 8.3 of Billingsley to the a…
Besov regularity of the uniform empirical process
Gane Samb Lo, Ahmadou Bamba Sow
The paths of Brownian motion have been widely studied in the recent years relatively in Besov spaces $B_{p, \infty}^\a$. The results are the same as to the Brownian bridge. In fact…