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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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Documents 60G44 | enregistrements trouvés : 62

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

Ecole d'été de probabilités de Saint-Flour XII Dudley, R. M. ; Kunita, H. ; Ledrappier , F. ; Hennequin, P. L. | Springer-Verlag 1984 Nouveau

Processus aléatoires a deux indices :colloque E.N.S.T.-C.N.E.T.#Juin 30 - Juil. 1 Korezlioglu, K. ; Mazziotto, G. ; Szpirglas, J. | Springer-Verlag 1980 Nouveau

Séminaire de probabilités XIV, 1978/79 Azema, J. ; Yor, M. | Springer-Verlag 1980 Nouveau

Lecture in probability and statistics :lectures given at the winter school in probability and statistics held in siantago de chile Del Pino, G. ; Rebolledo, R. | Springer-Verlag 1985 Nouveau

Statistical inference from stochastic processes :proceedings of the a.m.s.-i.m.a.-s.i.a.m. joint summer research conference on... held at cornell university#Aug. 9-15 Prabhu, N. U. | American Mathematical Society 1988 Nouveau

Statistics and control of random processes Novikov, A. A. ; Shiryaev, A. N. | American Mathematical Society 1994 Nouveau

Mathematical financeproceedings of the period of a workshop of the 1992-93 IMA program on control theory Davis, Mark H. A. ; Duffie, Darrell ; Fleming, Wendell H. ; Shreve, Steven E. | Springer 1995 Nouveau

Lectures on probability theory and statistics :Ecole d'Ete de probabilité de Saint-Flour XXVIII - 1998 Emery, M. ; Nemirovsky, A. S. ; Voiculescu, D. ; Bernard, P. | Springer 2000 Nouveau

Séminaire Bourbaki. Vol. 2000/2001 :exposés 880-893 | Société Mathématique de France 1998 Nouveau

Séminaire de probabilités XLIIIPoitiers # juin 2009 Donati-Martin, Catherine ; Lejay, Antoine ; Rouault, Alain | Springer 2011 Nouveau

Arbitrages in a progressive enlargement of filtration Jeanblanc, Monique | CIRM Nouveau

Probabilités et potentiel :chapitre V a VIII Dellacherie, Claude ; Meyer, Paul Andre | Hermann 1980 Nouveau

Inequalities for stopped brownian motion Van Der Vecht, D. P. | Centre For Mathematics And Computer Science 1986 Nouveau

Radically elementary probability theory Nelson, Edward | Princeton University Press 1987 Nouveau

Two-parameter martingales and their quadratic variation Imkeller, Peter | Springer-Verlag 1988 Nouveau

Stochastic integration and differential equations :A new approach Protter, Philip | Springer-Verlag 1990 Nouveau

A course on point processes Reiss, R. D. | Springer-Verlag 1993 Nouveau

Processus aléatoires gaussiens Ibrahimov, I. ; Rozanov, Y. ; Sokova, A. | Editions Mir 1974 Nouveau

Some topics in probability and analysis GUNDY , Richard F. | American Mathematical Society 1989 Nouveau

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Processus aléatoires a deux indices :
colloque E.N.S.T.-C.N.E.T.#Juin 30 - Juil. 1 Korezlioglu, K. ; Mazziotto, G. ; Szpirglas, J. | Springer-Verlag 1980 Nouveau

Lecture in probability and statistics :
lectures given at the winter school in probability and statistics held in siantago de chile Del Pino, G. ; Rebolledo, R. | Springer-Verlag 1985 Nouveau

Statistical inference from stochastic processes :
proceedings of the a.m.s.-i.m.a.-s.i.a.m. joint summer research conference on... held at cornell university#Aug. 9-15 Prabhu, N. U. | American Mathematical Society 1988 Nouveau

Mathematical finance
proceedings of the period of a workshop of the 1992-93 IMA program on control theory Davis, Mark H. A. ; Duffie, Darrell ; Fleming, Wendell H. ; Shreve, Steven E. | Springer 1995 Nouveau

Lectures on probability theory and statistics :
Ecole d'Ete de probabilité de Saint-Flour XXVIII - 1998 Emery, M. ; Nemirovsky, A. S. ; Voiculescu, D. ; Bernard, P. | Springer 2000 Nouveau

Séminaire Bourbaki. Vol. 2000/2001 :
exposés 880-893 | Société Mathématique de France 1998 Nouveau

Séminaire de probabilités XLIII
Poitiers # juin 2009 Donati-Martin, Catherine ; Lejay, Antoine ; Rouault, Alain | Springer 2011 Nouveau

Probabilités et potentiel :
chapitre V a VIII Dellacherie, Claude ; Meyer, Paul Andre | Hermann 1980 Nouveau

Stochastic integration and differential equations :
A new approach Protter, Philip | Springer-Verlag 1990 Nouveau