Simatos, Florian
Functional limit theorems, branching processes and stochastic networks.
(2016)
[HDR]
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(Document in English)
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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 |
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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 On: | 27 Nov 2017 16:10 |
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