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Verga, Federica (2019) Analysis of extremes in the branching Brownian motion. [Magistrali biennali]

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In my thesis, I study the extremal process of the branching Brownian motion. I am interested in a model in which particles are independent, move in space according to a Brownian motion and branch. To study the extremal process, I first introduce some basic definitions and facts on extreme value theory. Then, I define branching random walks and branching Brownian motion. I first study the maximum of both models and achieve important results. After that I focus on the extremal process of the branching Brownian motion, which is studied through a point process. The main theorem tells us that such a process converges to a Poisson cluster point process in the limit of large times. The thesis also contains a deep study of the paths of extremal particles: the result shows that such particles can move only in an admissible region that can be determined. Moreover, I prove an interesting theorem on the genealogy of the extremal particles: in the limit of large times, they descend with overwhelming probability from ancestors having split either within a distance of order 1 from time 0 or of order 1 from time t.

Item Type:Magistrali biennali
Corsi di Diploma di Laurea:Scuola di Scienze > Matematica
Uncontrolled Keywords: branching Brownian motion
Subjects:Area 01 - Scienze matematiche e informatiche > MAT/06 Probabilità e statistica matematica
Codice ID:62427
Relatore:Bianchi, Alessandra
Data della tesi:19 April 2019
Biblioteca:Polo di Scienze > Biblioteca di Matematica
Tipo di fruizione per il documento:on-line per i full-text
Tesi sperimentale (Si) o compilativa (No)?:No

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