Tesis doctorales: TESEO

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Ministerio de Universidades - Gobierno de España

Título: MODELS FOR BACTERIOPHAGE SYSTEMS, WEAK CONVERGENCE OF GAUSSIAN PROCESSES AND L2 MODULUS OF BROWNIAN LOCAL TIME.
Autor: Bascompte Viladrich, David
Universidad: Universidad Autónoma de Barcelona
Departamento: MATEMATICAS
Fecha de Lectura: 09/12/2013
Mención Europeo / Mención Internacional: Concedido
Programa de doctorado: Doctorat en Matemàtiques
Dirección:
- BARDINA SIMORRA, XAVIER (DIRECTOR)
Tribunal:
- JOLIS GIMÉNEZ, MARÍA (PRESIDENTE)
- MARQUEZ CARRERAS, DAVID (SECRETARIO)
- FERRANTE, MARCO (VOCAL)
Descriptores:
- PROCESOS ESTOCASTICOS
- TEOREMAS DEL LIMITE
- APLICACION DE LA PROBABILIDAD
- BIOMATEMATICAS
Localización: BIBLIOTECA DE COMUNICACIÓN Y HEMEROTECA GENERAL UAB

2013bascomodel.pdf

Marcador: https://www.educacion.gob.es/teseo/mostrarRef.do?ref=1055139Añadir a favoritos.
Resumen:
In this dissertation three different problems are treated. In Chapter 1 we construct two families of processes that converge, in the sense of the finite dimensional distributions, towards two independent Gaussian processes. Chapter 2 is devoted to the study of a model of bacteriophage treatments for bacterial infections. Finally, in Chapter 3 we study some aspects of the L2 modulus of continuity of Brownian local time. In the first chapter we consider two independent Gaussian processes that can be represented in terms of a stochastic integral of a deterministic kernel with respect to the Wiener process and we construct, from a single Poisson process, two families of processes that converge, in the sense of the finite dimensional distributions, towards these Gaussian processes. We will use this result to prove convergence in law results towards some other processes, like sub-fractional Brownian motion. In Chapter 2 we construct and study several models that pretend to study how will behave a treatment of bateriophages in some farm animals. This problem has been brought to our attention by the Molecular Biology Group of the Department of Genetics and Microbiology at the Universitat Autònoma de Barcelona. Starting from a basic model, we will study several variations, first from a deterministic point of view, finding several results on equilibria and stability, and later in a noisy context, producing concentration type results. Finally, in Chapter 3 we shall study the decomposition on Wiener chaos of the L2 modulus of continuity of the Brownian local time. More precisely, we shall find a Central Limit Theorem for each Wiener chaos element of the L2 modulus of continuity of the Brownian local time. This result provides us with an example of a family of random variables that is convergent in law to a Normal distribution, but its chaos elements of even order do not converge.

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