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Your search keyword '"Abraham, Romain"' showing total 6 results
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6 results on '"Abraham, Romain"'

1. Reversal property of the Brownian tree.

Author

Abraham, Romain and Delmas, Jean-François

Subjects
*BROWNIAN motion, *INFINITY (Mathematics), *BRANCHING processes, *INVARIANTS (Mathematics), *MATHEMATICS
Abstract

We consider the Brownian tree introduced by Aldous and the associated Q-process which consists in an infinite spine on which are grafted independent Brownian trees. We present a reversal procedure on these trees that consists in looking at the tree downward from its top: the branching points becoming leaves and leaves becoming branching points. We prove that the distribution of this tree is invariant under this reversal procedure, which provides a better understanding of previous results from Bi and Delmas (2016). [ABSTRACT FROM AUTHOR]

Published
2018
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2. Fragmentation associated with Lévy processes using snake.

Author

Abraham, Romain and Delams, Jean-François

Subjects
*PROBABILITY measures, *RANDOM walks, *LEVY processes, *MATHEMATICS, *MARKOV processes, *NUMERICAL analysis
Abstract

We consider the height process of a Lévy process with no negative jumps, and its associated continuous tree representation. Using Lévy snake tools developed by Le Gall-Le Jan and Duquesne-Le Gall, with an underlying Poisson process, we construct a fragmentation process, which in the stable case corresponds to the self-similar fragmentation described by Miermont. For the general fragmentation process we compute a family of dislocation measures as well as the law of the size of a tagged fragment. We also give a special Markov property for the snake which is of its own interest. [ABSTRACT FROM AUTHOR]

Published
2008
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3. Some Properties of Stationary Continuous State Branching Processes

Author

Romain Abraham, Jean-François Delmas, Hui He, Abraham, Romain, Institut Denis Poisson (IDP), Université d'Orléans (UO)-Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS), Centre d'Enseignement et de Recherche en Mathématiques, Informatique et Calcul Scientifique (CERMICS), Institut National de Recherche en Informatique et en Automatique (Inria)-École des Ponts ParisTech (ENPC), School of Mathematical Sciences [Beijing] (SMS), Beijing Normal University (BNU), Partially supported by NSFC (No. 11671041 and 11531001), Centre National de la Recherche Scientifique (CNRS)-Université de Tours (UT)-Université d'Orléans (UO), and Centre National de la Recherche Scientifique (CNRS)-Université de Tours-Université d'Orléans (UO)

Subjects
Statistics and Probability, [MATH.MATH-PR] Mathematics [math]/Probability [math.PR], Ancestral process, Population, Markov process, Quasi-stationary distribution, 01 natural sciences, Branching (linguistics), 010104 statistics & probability, symbols.namesake, Extant taxon, Genealogical Tree, Mathematics::Probability, Fixed time, MSC 2010 : 60J80, 60J27, 92D25, FOS: Mathematics, Quantitative Biology::Populations and Evolution, Statistical physics, 0101 mathematics, education, Branching process, Mathematics, education.field_of_study, Applied Mathematics, 010102 general mathematics, Probability (math.PR), State (functional analysis), Genealogical tree, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Continuous branching process with immigration, Modeling and Simulation, symbols, Mathematics - Probability
Abstract

We consider the genealogical tree of a stationary continuous state branching process with immigration. For a sub-critical stable branching mechanism, we consider the genealogical tree of the extant population at some fixed time and prove that, up to a deterministic time-change, it is distributed as a continuous-time Galton-Watson process with immigration. We obtain similar results for a critical stable branching mechanism when only looking at immigrants arriving in some fixed time-interval. For a general sub-critical branching mechanism, we consider the number of individuals that give descendants in the extant population. The associated processes (forward or backward in time) are pure-death or pure-birth Markov processes, for which we compute the transition rates., Comment: 31 pages, 1 figure

Published
2021

4. Reversal property of the Brownian tree

Author

Romain Abraham, Jean-François Delmas, Mathématiques - Analyse, Probabilités, Modélisation - Orléans (MAPMO), Université d'Orléans (UO)-Centre National de la Recherche Scientifique (CNRS), Centre d'Enseignement et de Recherche en Mathématiques, Informatique et Calcul Scientifique (CERMICS), Institut National de Recherche en Informatique et en Automatique (Inria)-École des Ponts ParisTech (ENPC), ANR-14-CE25-0014,GRAAL,GRaphes et Arbres ALéatoires(2014), Centre National de la Recherche Scientifique (CNRS)-Université d'Orléans (UO), Abraham, Romain, and Appel à projets générique - GRaphes et Arbres ALéatoires - - GRAAL2014 - ANR-14-CE25-0014 - Appel à projets générique - VALID

Subjects
Statistics and Probability, [MATH.MATH-PR] Mathematics [math]/Probability [math.PR], Probability (math.PR), 010102 general mathematics, Branching points, 01 natural sciences, Combinatorics, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], 010104 statistics & probability, Mathematics::Probability, FOS: Mathematics, 0101 mathematics, Invariant (mathematics), Brownian tree, Mathematics - Probability, Brownian motion, Mathematics
Abstract

We consider the Brownian tree introduced by Aldous and the associated Q-process which consists in an infinite spine on which are grafted independent Brownian trees. We present a reversal procedure on these trees that consists in looking at the tree downward from its top: the branching points becoming leaves and leaves becoming branching points. We prove that the distribution of the tree is invariant under this reversal procedure, which provides a better understanding of previous results from Bi and Delmas (2016)., Comment: This is the second version of the preprint arXiv:1612.03715 that has been splitted into two papers

Published
2018

5. Forward-backward stochastic differential equations and PDE with gradient dependent second order coefficients

Author

Romain Abraham, Olivier Riviere, Mathématiques - Analyse, Probabilités, Modélisation - Orléans (MAPMO), Centre National de la Recherche Scientifique (CNRS)-Université d'Orléans (UO), Mathématiques Appliquées Paris 5 (MAP5 - UMR 8145), Université Paris Descartes - Paris 5 (UPD5)-Institut National des Sciences Mathématiques et de leurs Interactions (INSMI)-Centre National de la Recherche Scientifique (CNRS), Mathématiques - Analyse, Probabilités, Modélisation - Orléans ( MAPMO ), Université d'Orléans ( UO ) -Centre National de la Recherche Scientifique ( CNRS ), Mathématiques Appliquées à Paris 5 ( MAP5 - UMR 8145 ), Université Paris Descartes - Paris 5 ( UPD5 ) -Institut National des Sciences Mathématiques et de leurs Interactions-Centre National de la Recherche Scientifique ( CNRS ), Abraham, Romain, and Université d'Orléans (UO)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Statistics and Probability, [MATH.MATH-PR] Mathematics [math]/Probability [math.PR], Differential equation, Mathematical analysis, 02 engineering and technology, 01 natural sciences, Stochastic partial differential equation, Examples of differential equations, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], 010104 statistics & probability, symbols.namesake, Stochastic differential equation, Elliptic partial differential equation, 0202 electrical engineering, electronic engineering, information engineering, Runge–Kutta method, symbols, 020201 artificial intelligence & image processing, 0101 mathematics, [ MATH.MATH-PR ] Mathematics [math]/Probability [math.PR], Mathematics, Numerical partial differential equations, Separable partial differential equation
Abstract

We consider a system of fully coupled forward-backward stochastic differential equations. First we generalize the results of Pardoux-Tang [7] concerning the regularity of the solutions with respect to initial conditions. Then, we prove that in some particular cases this system leads to a probabilistic representation of solutions of a second-order PDE whose second order coefficients depend on the gradient of the solution. We then give some examples in dimension 1 and dimension 2 for which the assumptions are easy to check.

Published
2006

6. Representations of the Brownian snake with drift

Author

Romain Abraham, Laurent Serlet, Graffigne, Christine, Mathématiques - Analyse, Probabilités, Modélisation - Orléans (MAPMO), Centre National de la Recherche Scientifique (CNRS)-Université d'Orléans (UO), Mathématiques Appliquées Paris 5 (MAP5 - UMR 8145), Université Paris Descartes - Paris 5 (UPD5)-Institut National des Sciences Mathématiques et de leurs Interactions (INSMI)-Centre National de la Recherche Scientifique (CNRS), Mathématiques - Analyse, Probabilités, Modélisation - Orléans ( MAPMO ), Université d'Orléans ( UO ) -Centre National de la Recherche Scientifique ( CNRS ), Mathématiques Appliquées à Paris 5 ( MAP5 - UMR 8145 ), Université Paris Descartes - Paris 5 ( UPD5 ) -Institut National des Sciences Mathématiques et de leurs Interactions-Centre National de la Recherche Scientifique ( CNRS ), Abraham, Romain, and Université d'Orléans (UO)-Centre National de la Recherche Scientifique (CNRS)

Subjects
[MATH.MATH-PR] Mathematics [math]/Probability [math.PR], Geometric Brownian motion, Fractional Brownian motion, Stochastic process, 010102 general mathematics, Mathematical analysis, Ornstein–Uhlenbeck process, Brownian excursion, 01 natural sciences, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], 010104 statistics & probability, Mathematics::Probability, Reflected Brownian motion, Diffusion process, Novikov's condition, Statistical physics, 0101 mathematics, [ MATH.MATH-PR ] Mathematics [math]/Probability [math.PR], Mathematics
Abstract

We consider a path-valued process which is a generalization of the classical Brownian snake introduced by Le Gall. More precisely we add a drift term b to the lifetime process, which may depends on...

Published
2002

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