NBC News Scripts
WBAP-TV (Television station : Fort Worth, Tex.)
1954-12-31
Search results
32 records were found.
Branching process in random environment (BPRE) Yaglom distribution Q-process Random walk with negative drift
We approximate stochastic processes in finite dimension by dynamical systems. We provide trajectorial estimates which are uniform with respect to the initial condition for a well chosen distance. This relies on some non-expansivity property of the flow, which allows to deal with non-Lipschitz vector fields. We use the stochastic calculus and follow the martingale technics initiated in Berestycki and al [5] to control the fluctuations. Our main applications deal with the short time behavior of stochastic processes starting from large initial values. We state general properties on the coming down from infinity of one-dimensional SDEs, with a focus on stochastically monotone processes. In particular, we recover and complement known results on Lambda-coalescent and birth and death processes. Moreover, using Poincaré...
We consider a branching model in discrete time for structured population in varying environment. Each individual has a trait, which belongs to some general state space and both the reproduction law and the trait inherited by the offsprings may depend on the trait of the mother and the environment.We study the long time behavior of the population and the ancestral lineage of typical individuals under general assumptions. We focus on the growth rate and the trait distribution among the population for large time and provide some estimations of the local densities. A key role is played by well chosen (possibly non-homogeneous) Markov chains. It relies in particular on an extension of many-to-one formula and the analysis of the genealogy, in the vein of the spine decomposition. The applications use the spectral gap of the mean o...
We consider a branching model for a population of dividing cells infected by parasites. Each cell receives parasites by inheritance from its mother cell and independent contamination from outside the population. Parasites multiply randomly inside the cell and are shared randomly between the two daughter cells when the cell divides. The law of the number of parasites which contaminate a given cell depends only on whether the cell is already infected or not. We determine the asymptotic behavior of the number of parasites in a cell line, which follows a branching process in random environment with state dependent immigration. We then derive a law of large numbers for the asymptotic proportions of cells with a given number of parasites. The main tools are branching processes in random environment and laws of large numbers for Markov tree.
Dans une première partie, j'étudie un processus de stockage de données en temps continu où le disque dur est identifié à la droite réelle. Ce modèle est une version continu du problème original de Parking de Knuth. Ici l'arrivée des fichiers est Poissonienne et le fichier se stocke dans les premiers espaces libres à droite de son point d'arrivée, quitte à se fragmenter. Dans un premier temps, je construis le modèle et donne une caractérisation géométrique et analytique de la partie du disque recouverte au temps t. Ensuite j'étudie les régimes asymptotiques au moment de saturation du disque. Enfin, je décris l'évolution en temps d'un block de données typique. La deuxième partie est constituée de l'étude de processus de branchement, motivée par des questions d'infection cellulaire. Dans un premier temps, je considère un processus de bran...
We consider a branching model introduced by Kimmel for cell division with parasite infection. Cells contain proliferating parasites which are shared randomly between the two daughter cells when they divide. We determine the probability that the organism recovers, meaning that the asymptotic proportion of contaminated cells vanishes. We study the tree of contaminated cells, give the asymptotic number of contaminated cells and the asymptotic proportions of contaminated cells with a given number of parasites. This depends on domains inherited from the behavior of branching processes in random environment (BPRE) and given by the bivariate value of the means of parasite offsprings. In one of these domains, the convergence of proportions holds in probability, the limit is deterministic and given by the Yaglom quasistationary distribution. Mo...
We consider a generalized version in continuous time of the parking problem of Knuth. Files arrive following a Poisson point process and are stored on a hardware identified with the real line. We specify the distribution of the space of unoccupied locations at a fixed time and give its asymptotics when the hardware is becoming full.
We approximate stochastic processes in finite dimension by dynamical systems. We provide trajectorial estimates which are uniform with respect to the initial condition for a well chosen distance. This relies on some non-expansivity property of the flow, which allows to deal with non-Lipschitz vector fields. We use the stochastic calculus and follow the martingale technics initiated in Berestycki and al [5] to control the fluctuations. Our main applications deal with the short time behavior of stochastic processes starting from large initial values. We state general properties on the coming down from infinity of one-dimensional SDEs, with a focus on stochastically monotone processes. In particular, we recover and complement known results on Lambda-coalescent and birth and death processes. Moreover, using Poincaré...
The asymptotic behavior of a subcritical Branching Process in Random Environment (BPRE) starting with several particles depends on whether the BPRE is strongly subcritical (SS), intermediate subcritical (IS) or weakly subcritical (WS). %Descendances of particles for BPRE are not independent. In the (SS+IS) case, the asymptotic probability of survival is proportional to the initial number of particles, and conditionally on the survival of the population, only one initial particle survives $a.s.$ These two properties do not hold in the (WS) case and different asymptotics are established, which require new results on random walks with negative drift. We provide an interpretation of these results by characterizing the sequence of environments selected when we condition on the survival of particles. This also raises the problem of the depen...
We consider a generalized version in continuous time of the parking problem of Knuth. Files arrive following a Poisson point process and are stored on a hardware identified with the real line, at the right of their arrival point. We study here the evolution of the extremities of the data block straddling $0$, which is empty at time $0$ and is equal to $\RRR$ at a deterministic time.
