11 citations · 11 across the 4 of their papers we have counts for
5 papers
Local times and excursions for self-similar Markov trees
Jean Bertoin, Armand Riera, Alejandro Rosales-Ortiz
This work builds upon the recent monograph [5] on self-similar Markov trees. A self-similar Markov tree is a random real tree equipped with a function from the tree to …
Excursion theory for Markov processes indexed by Levy trees
Armand Riera, Alejandro Rosales-Ortiz
We develop an excursion theory that describes the evolution of a Markov process indexed by a Levy tree away from a regular and instantaneous point of the state space. The theor…
Noise Reinforced Lévy Processes: Lévy-Itô Decomposition and Applications
Alejandro Rosales-Ortiz
A step reinforced random walk is a discrete time process with memory such that at each time step, with fixed probability , it repeats a previously performed step chose…
The structure of the local time of Markov processes indexed by Levy trees
Armand Riera, Alejandro Rosales-Ortiz
We construct the analogue of the local time -- at a fixed point -- for Markov processes indexed by Levy trees. We start by proving that Markov processes indexed by Levy trees s…
Joint invariance principles for random walks with positively and negatively reinforced steps
Marco Bertenghi, Alejandro Rosales-Ortiz
Given a random walk with typical step distributed according to some fixed law and a fixed parameter , the associated positively step-reinforced random walk is…