The Experts below are selected from a list of 282 Experts worldwide ranked by ideXlab platform
Amaury Lambert - One of the best experts on this subject based on the ideXlab platform.
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Branching processes seen from their Extinction Time via path decompositions of reflected Lévy processes
Electronic Journal of Probability, 2018Co-Authors: Miraine Dávila Felipe, Amaury LambertAbstract:We consider a spectrally positive Levy process X that does not drift to +∞, viewed as coding for the genealogical structure of a (sub)critical branching process, in the sense of a contour or exploration process [34, 29]. We denote by I the past infimum process defined for each t≥0 by It:=inf[0,t]X and we let γ be the unique Time at which the excursion of the reflected process X−I away from 0 attains its supremum. We prove that the pre-γ and the post-γ subpaths of this excursion are invariant under space-Time reversal, which has several other consequences in terms of duality for excursions of Levy processes. It implies in particular that the local Time process of this excursion is also invariant when seen backward from its height. As a corollary, we obtain that some (sub)critical branching processes such as the binary, homogeneous (sub)critical Crump-Mode-Jagers (CMJ) processes and the excursion away from 0 of the critical Feller diffusion, which is the width process of the continuum random tree, are invariant under Time reversal from their Extinction Time.
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Branching processes seen from their Extinction Time via path decompositions of reflected Lévy processes
Electronic Journal of Probability, 2018Co-Authors: Miraine Dávila Felipe, Amaury LambertAbstract:We consider a spectrally positive Lévy process X that does not drift to +∞, viewed as coding for the genealogical structure of a (sub)critical branching process, in the sense of a contour or exploration process [34, 29]. We denote by I the past infimum process defined for each t≥0 by It:=inf[0,t]X and we let γ be the unique Time at which the excursion of the reflected process X−I away from 0 attains its supremum. We prove that the pre-γ and the post-γ subpaths of this excursion are invariant under space-Time reversal, which has several other consequences in terms of duality for excursions of Lévy processes. It implies in particular that the local Time process of this excursion is also invariant when seen backward from its height. As a corollary, we obtain that some (sub)critical branching processes such as the binary, homogeneous (sub)critical Crump-Mode-Jagers (CMJ) processes and the excursion away from 0 of the critical Feller diffusion, which is the width process of the continuum random tree, are invariant under Time reversal from their Extinction Time.
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Branching processes seen from their Extinction Time via path decompositions of reflected L\'evy processes
arXiv: Probability, 2016Co-Authors: Miraine Dávila Felipe, Amaury LambertAbstract:We consider a spectrally positive L\'evy process $X$ that does not drift to $+\infty$, coding for the genealogical structure of a (sub)critical branching process, in the sense of a contour or exploration process \cite{GaJa98,Lam10}. Denote by $I$ the past infimum process defined for each $t\geq 0$ by $I_t:= \inf_{[0,t]} X$. Let $\gamma$ be the unique Time at which the excursion of the reflected process $X-I$ away from 0 attains its supremum. We prove that the pre-$\gamma$ and the post-$\gamma$ subpaths of this excursion are invariant under space-Time reversal. This implies in particular that the local Time process of this excursion is also invariant when seen backward from its height. These results show that some (sub)critical branching processes such as the (sub)critical Crump-Mode-Jagers (CMJ) processes and the excursion away from 0 of the critical Feller diffusion, which is the width process of the continuum random tree, are invariant under Time reversal from their Extinction Time.
Peter Windridge - One of the best experts on this subject based on the ideXlab platform.
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The Extinction Time of a subcritical branching process related to the SIR epidemic on a random graph
Journal of Applied Probability, 2015Co-Authors: Peter WindridgeAbstract:We give an exponential tail approximation for the Extinction Time of a subcritical multitype branching process arising from the SIR epidemic model on a random graph with given degrees, where the type corresponds to the vertex degree. As a corollary we obtain a Gumbel limit law for the Extinction Time, when beginning with a large population. Our contribution is to allow countably many types (this corresponds to unbounded degrees in the random graph epidemic model, as the number of vertices tends to∞). We only require a second moment for the offspring-type distribution featuring in our model.
Corey J A Bradshaw - One of the best experts on this subject based on the ideXlab platform.
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robust estimates of Extinction Time in the geological record
Quaternary Science Reviews, 2012Co-Authors: Corey J A Bradshaw, Chris S M Turney, Alan Cooper, Barry W. BrookAbstract:Abstract The rate at which a once-abundant population declines in density prior to local or global Extinction can strongly influence the precision of statistical estimates of Extinction Time. Here we report the development of a new, robust method of inference which accounts for these potential biases and uncertainties, and test it against known simulated data and dated Pleistocene fossil remains (mammoths, horses and Neanderthals). Our method is a Gaussian-resampled, inverse-weighted McInerny et al. (GRIWM) approach which weights observations inversely according to their temporal distance from the last observation of a species' confirmed occurrence, and for dates with associated radiometric errors, is able to sample individual dates from an underlying fossilization probability distribution. We show that this leads to less biased estimates of the ‘true’ Extinction date. In general, our method provides a flexible tool for hypothesis testing, including inferring the probability that the Extinctions of pairs or groups of species overlap, and for more robustly evaluating the relative likelihood of different Extinction drivers such as climate perturbation and human exploitation.
Miraine Dávila Felipe - One of the best experts on this subject based on the ideXlab platform.
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Branching processes seen from their Extinction Time via path decompositions of reflected Lévy processes
Electronic Journal of Probability, 2018Co-Authors: Miraine Dávila Felipe, Amaury LambertAbstract:We consider a spectrally positive Lévy process X that does not drift to +∞, viewed as coding for the genealogical structure of a (sub)critical branching process, in the sense of a contour or exploration process [34, 29]. We denote by I the past infimum process defined for each t≥0 by It:=inf[0,t]X and we let γ be the unique Time at which the excursion of the reflected process X−I away from 0 attains its supremum. We prove that the pre-γ and the post-γ subpaths of this excursion are invariant under space-Time reversal, which has several other consequences in terms of duality for excursions of Lévy processes. It implies in particular that the local Time process of this excursion is also invariant when seen backward from its height. As a corollary, we obtain that some (sub)critical branching processes such as the binary, homogeneous (sub)critical Crump-Mode-Jagers (CMJ) processes and the excursion away from 0 of the critical Feller diffusion, which is the width process of the continuum random tree, are invariant under Time reversal from their Extinction Time.
Miraine Dávila Felipe - One of the best experts on this subject based on the ideXlab platform.
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Branching processes seen from their Extinction Time via path decompositions of reflected Lévy processes
Electronic Journal of Probability, 2018Co-Authors: Miraine Dávila Felipe, Amaury LambertAbstract:We consider a spectrally positive Levy process X that does not drift to +∞, viewed as coding for the genealogical structure of a (sub)critical branching process, in the sense of a contour or exploration process [34, 29]. We denote by I the past infimum process defined for each t≥0 by It:=inf[0,t]X and we let γ be the unique Time at which the excursion of the reflected process X−I away from 0 attains its supremum. We prove that the pre-γ and the post-γ subpaths of this excursion are invariant under space-Time reversal, which has several other consequences in terms of duality for excursions of Levy processes. It implies in particular that the local Time process of this excursion is also invariant when seen backward from its height. As a corollary, we obtain that some (sub)critical branching processes such as the binary, homogeneous (sub)critical Crump-Mode-Jagers (CMJ) processes and the excursion away from 0 of the critical Feller diffusion, which is the width process of the continuum random tree, are invariant under Time reversal from their Extinction Time.
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Branching processes seen from their Extinction Time via path decompositions of reflected L\'evy processes
arXiv: Probability, 2016Co-Authors: Miraine Dávila Felipe, Amaury LambertAbstract:We consider a spectrally positive L\'evy process $X$ that does not drift to $+\infty$, coding for the genealogical structure of a (sub)critical branching process, in the sense of a contour or exploration process \cite{GaJa98,Lam10}. Denote by $I$ the past infimum process defined for each $t\geq 0$ by $I_t:= \inf_{[0,t]} X$. Let $\gamma$ be the unique Time at which the excursion of the reflected process $X-I$ away from 0 attains its supremum. We prove that the pre-$\gamma$ and the post-$\gamma$ subpaths of this excursion are invariant under space-Time reversal. This implies in particular that the local Time process of this excursion is also invariant when seen backward from its height. These results show that some (sub)critical branching processes such as the (sub)critical Crump-Mode-Jagers (CMJ) processes and the excursion away from 0 of the critical Feller diffusion, which is the width process of the continuum random tree, are invariant under Time reversal from their Extinction Time.
