6 results on '"Abraham, Romain"'
Search Results
2. Some properties of the exit measure for super-Brownian motion
- Author
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Abraham, Romain, Delmas, Jean-François, 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), Centre National de la Recherche Scientifique (CNRS)-Université d'Orléans (UO), and Abraham, Romain
- Subjects
[MATH.MATH-PR]Mathematics [math]/Probability [math.PR] ,[MATH.MATH-PR] Mathematics [math]/Probability [math.PR] - Published
- 2002
3. Some Properties of Stationary Continuous State Branching Processes
- Author
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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
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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
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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
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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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