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# Documents  Bertoin, Jean | enregistrements trouvés : 4

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## Martingales in self-similar growth-fragmentations and their applications Bertoin, Jean | CIRM H

Post-edited

Research talks;Probability and Statistics

This talk is based on a work jointly with Timothy Budd (Copenhagen), Nicolas Curien (Orsay) and Igor Kortchemski (Ecole Polytechnique).
Consider a self-similar Markov process $X$ on $[0,\infty)$ which converges at infinity a.s. We interpret $X(t)$ as the size of a typical cell at time $t$, and each negative jump as a birth event. More precisely, if ${\Delta}X(s) = -y < 0$, then $s$ is the birth at time of a daughter cell with size $y$ which then evolves independently and according to the same dynamics. In turn, daughter cells give birth to granddaughter cells each time they make a negative jump, and so on.
The genealogical structure of the cell population can be described in terms of a branching random walk, and this gives rise to remarkable martingales. We analyze traces of these mar- tingales in physical time, and point at some applications for self-similar growth-fragmentation processes and for planar random maps.
This talk is based on a work jointly with Timothy Budd (Copenhagen), Nicolas Curien (Orsay) and Igor Kortchemski (Ecole Polytechnique).
Consider a self-similar Markov process $X$ on $[0,\infty)$ which converges at infinity a.s. We interpret $X(t)$ as the size of a typical cell at time $t$, and each negative jump as a birth event. More precisely, if ${\Delta}X(s) = -y < 0$, then $s$ is the birth at time of a daughter cell with size $y$ which then ...

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## Levy processes Bertoin, Jean | Cambridge University Press 1996

Ouvrage

- 266 p.
ISBN 978-0-521-64632-1

Cambridge tracts in mathematics , 0121

Localisation : Collection 1er étage

processus de Levy # processus de Markov # processus stochastiques # théorie des probabilités # théorie du potentiel

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## Random fragmentation and coagulation processes Bertoin, Jean | Cambridge University Press 2006

Ouvrage

- 280 p.
ISBN 978-0-521-86728-3

Cambridge studies in advanced mathematics , 0102

Localisation : Ouvrage RdC (BERT)

probabilités # probabilités combinatoriales # processus autosimilaire # théorème limite fort # processus de Markov # processus de branchement # arbre aléatoire # mesure de Poisson # limite hydrodynamique # équation de Smoluchowski

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## Lévy matters I.Recent progress in theory and applications: foundations, trees and numerical issues in finance.With a short biography of Paul Lévy by Jean Jacod Barndorff-Nielsen, Ole E. ; Bertoin, Jean ; Jacod, Jean ; Klüppelberg, Claudia ; Duquesne, Thomas ; Reichmann, Oleg ; Sato, Ken-Iti ; Schwab, Christoph | Springer 2010

Ouvrage

- xiv; 198 p.
ISBN 978-3-642-14006-8

Lecture notes in mathematics , 2001

Localisation : Collection 1er étage

Paul Lévy # processus de Lévy # processus ramifié # arbre # finances # probabilités # processus à incréments indépendant # file d'attente # biographie

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