84 citations · 409 across the 25 of their papers we have counts for
25 papers
Critical branching processes with immigration: scaling limits of local extinction sets
Aleksandar Mijatović, Benjamin Povar, Gerónimo Uribe Bravo
We establish the joint scaling limit of a critical Bienaymé-Galton-Watson process with immigration (BGWI) and its (counting) local time at zero to the corresponding self-similar co…
The Sticky Lévy Process as a solution to a Time Change Equation
Miriam Ramírez, Gerónimo Uribe Bravo
Stochastic Differential Equations (SDEs) were originally devised by Itô to provide a pathwise construction of diffusion processes. A less explored approach to represent them is thr…
An algorithm for simulating Brownian increments on a sphere
Aleksandar Mijatović, Veno Mramor, Gerónimo Uribe Bravo
This paper presents a novel formula for the transition density of the Brownian motion on a sphere of any dimension and discusses an algorithm for the simulation of the increments o…
On the profile of trees with a given degree sequence
Osvaldo Angtuncio, Gerónimo Uribe Bravo
A degree sequence is a sequence of non-negative integers satisfying . We are interested in the uniform distribution $\mathb…
-strong simulation of the convex minorants of stable processes and meanders
Jorge Ignacio González Cázares, Aleksandar Mijatović, Gerónimo Uribe Bravo
Using marked Dirichlet processes we characterise the law of the convex minorant of the meander for a certain class of Lévy processes, which includes subordinated stable and symmetr…
Invariance principles for local times in regenerative settings
Aleksandar Mijatović, Gerónimo Uribe Bravo
Consider a stochastic process , regenerative at a state which is instantaneous and regular. Let be a regenerative local time for at . Suppos…
Dini derivatives for Exchangeable Increment processes and applications
Osvaldo Angtuncio Hernández, Gerónimo Uribe Bravo
Let be an exchangeable increment (EI) process whose sample paths are of infinite variation. We prove that, for any fixed almost surely, \[ \limsup_{h\to 0 \pm} (X_{t+h}-X_t…
Geometrically Convergent Simulation of the Extrema of Lévy Processes
Jorge Ignacio González Cázares, Aleksandar Mijatović, Gerónimo Uribe Bravo
We develop a novel approximate simulation algorithm for the joint law of the position, the running supremum and the time of the supremum of a general Lévy process at an arbitrary f…
Random walks with preferential relocations and fading memory: a study through random recursive trees
Cécile Mailler, Gerónimo Uribe Bravo
Consider a stochastic process that behaves as a -dimensional simple and symmetric random walk, except that, with a certain fixed probability, at each step, it chooses instead to…
Exact Simulation of the Extrema of Stable Processes
Jorge Ignacio González Cázares, Aleksandar Mijatović, Gerónimo Uribe Bravo
We exhibit an exact simulation algorithm for the supremum of a stable process over a finite time interval using dominated coupling from the past (DCFTP). We establish a novel perpe…
Projections of spherical Brownian motion
Aleksandar Mijatović, Veno Mramor, Gerónimo Uribe Bravo
We obtain a stochastic differential equation (SDE) satisfied by the first coordinates of a Brownian motion on the unit sphere in . The SDE has non-Lipschit…
Totally Ordered Measured Trees and Splitting Trees with Infinite Variation II: Prolific Skeleton Decomposition
Amaury Lambert, Gerónimo Uribe Bravo
The first part of this paper ( arXiv:1607.02114 ) introduced splitting trees, those chronological trees admitting the self-similarity property where individuals give birth, at cons…
Totally Ordered Measured Trees and Splitting Trees with Infinite Variation
Amaury Lambert, Gerónimo Uribe Bravo
Combinatorial trees can be used to represent genealogies of asexual individuals. These individuals can be endowed with birth and death times, to obtain a so-called `chronological t…
The comb representation of compact ultrametric spaces
Amaury Lambert, Geronimo Uribe Bravo
We call a \emph{comb} a map , where is a compact interval, such that is finite for any . A comb induces a (pseudo)-distan…
Affine processes on and multiparameter time changes
Ma. Emilia Caballero, José Luis Pérez Garmendia, Gerónimo Uribe Bravo
We present a time change construction of affine processes with state-space . These processes were systematically studied in (Duffie, Filipović an…
Shifting processes with cyclically exchangeable increments at random
Loïc Chaumont, Gerónimo Uribe Bravo
We propose a path transformation which applied to a cyclically exchangeable increment process conditions its minimum to belong to a given interval. This path transformation is then…
Supercritical percolation on large scale-free random trees
Jean Bertoin, Geronimo Uribe Bravo
We consider Bernoulli bond percolation on a large scale-free tree in the supercritical regime, meaning informally that there exists a giant cluster with high probability. We obtain…
Local extinction in continuous-state branching processes with immigration
Clément Foucart, Gerónimo Uribe Bravo
The purpose of this article is to observe that the zero sets of continuous-state branching processes with immigration (CBI) are infinitely divisible regenerative sets. Indeed, they…
Convex minorants of random walks and Lévy processes
Josh Abramson, Jim Pitman, Nathan Ross +1
This article provides an overview of recent work on descriptions and properties of the convex minorant of random walks and Lévy processes which summarize and extend the literature…
Bridges of Lévy processes conditioned to stay positive
Gerónimo Uribe Bravo
We consider Kallenberg's hypothesis on the characteristic function of a Lévy process and show that it allows the construction of weakly continuous bridges of the Lévy process condi…
A Lamperti-type representation of continuous-state branching processes with immigration
M. Emilia Caballero, José Luis Pérez Garmendia, Gerónimo Uribe Bravo
Guided by the relationship between the breadth-first walk of a rooted tree and its sequence of generation sizes, we are able to include immigration in the Lamperti representation o…
The convex minorant of a Lévy process
Jim Pitman, Gerónimo Uribe Bravo
We offer a unified approach to the theory of convex minorants of Lévy processes with continuous distributions. New results include simple explicit constructions of the convex minor…
Markovian bridges: Weak continuity and pathwise constructions
Loïc Chaumont, Gerónimo Uribe Bravo
A Markovian bridge is a probability measure taken from a disintegration of the law of an initial part of the path of a Markov process given its terminal value. As such, Markovian b…
The falling appart of the tagged fragment and the asymptotic disintegration of the Brownian height fragmentation
Gerónimo Uribe Bravo
We present a further analysis of the fragmentation at heights of the normalized Brownian excursion. Specifically we study a representation for the mass of a tagged fragment in term…