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Functional limit theorems, branching processes and stochastic networks

Simatos, Florian Functional limit theorems, branching processes and stochastic networks. (2016) [HDR]

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Abstract

This manuscript describes some of the work I have been doing since 2010 and the end of my PhD. As the title suggests, it contains three main parts. 1. Functional limit theorems: Chapter 2 presents two theoretical results on the weak convergence of stochastic processes: one is a sufficient condition for the tightness of a sequence of stochastic processes and the other provides a sufficient condition for the weak convergence of a sequence of regenerative processes; 2. Branching processes: in Chapter 3, scaling limits of three particular types of branching processes are discussed: 1) Galton-Watson processes in varying environments, 2) binary and homogeneous Crump-Mode-Jagers processes and 3) Crump-Mode-Jagers processes with short edges;3. Stochastic networks: Chapter 4 presents three results on stochastic networks: 1) scaling limits of the M/G/1 Processor-Sharing queue length process, 2) study of a model of stochastic network with mobile customers and 3) heavy traffic delay performance of queue-based scheduling algorithms.

Item Type:HDR
Uncontrolled Keywords:
Institution:Université de Toulouse > Institut Supérieur de l'Aéronautique et de l'Espace - ISAE-SUPAERO (FRANCE)
Laboratory name:
Research Director:
Miclo, Laurent
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Deposited By: Florian Simatos
Deposited On:27 Nov 2017 16:10

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