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Applications des processus de Lévy et processus de branchement à des études motivées par l'informatique et la biologie

Abstract : First, I study a process for data storage in continuous time where the hardware is identified with the real line. This is a continous time version of the original Parking problem of Knuth, which has been by Flajolet, Chassaing and Louchard. Here, the arrival of files follows a Poisson point process and files are stored in the first free places at the right of their arrival point, and can be splitted into several parts. I begin by constructing this model and giving an analytic and geometric construction of the process. Then, I study asymptotics regimes at saturation of the hardware. Finally I describe the evolution in time of a typical data block. Secondly, I consider branching processes for questions motivated by biology. First, I determine limit theorems for subcritical branching processes in random environment, depending on the initial numbers of individuals. Then I consider a branching model for cell division with parasite infection, where the random cell follows a branching process in random environment. I give the probability of recovery of the organism, the asymptotic number of parasites and the asymptotic proportions of infected cells with a given number of parasites. These results depend on the subcriticality of the cell line. Finally, I add a random contamination by parasites from outside the cell population, which requires proving new results about branching processes in random environment with immigration.
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https://tel.archives-ouvertes.fr/tel-00339230
Contributor : Vincent Bansaye <>
Submitted on : Monday, November 17, 2008 - 12:37:31 PM
Last modification on : Wednesday, December 9, 2020 - 3:10:38 PM
Long-term archiving on: : Monday, June 7, 2010 - 8:40:30 PM

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  • HAL Id : tel-00339230, version 1

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Vincent Bansaye. Applications des processus de Lévy et processus de branchement à des études motivées par l'informatique et la biologie. Mathematics [math]. Université Pierre et Marie Curie - Paris VI, 2008. English. ⟨tel-00339230⟩

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