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Simulation and estimation of Lévy driven stochastic processes

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hdl:2117/106951

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Brull Borràs, Pere Miquel
Tutor / directorArratia Quesada, Argimiro AlejandroMés informacióMés informacióMés informació
Document typeBachelor thesis
Date2017-07
Rights accessOpen Access
Attribution-NonCommercial-NoDerivs 3.0 Spain
Except where otherwise noted, content on this work is licensed under a Creative Commons license : Attribution-NonCommercial-NoDerivs 3.0 Spain
Abstract
We carry on an exploration of Lévy processes, focusing on instrumental definitions that ease our way towards their simulation. Beginning with the basic Brownian motion and Poisson processes, we then explore algorithms to simulate Lévy processes, do maximum likelihood estimations, and follow this exploratory road studying a maximum likelihood methodology to estimate the parameters of a one dimensional stationary process of Ornstein Uhlenbeck type that is constructed via a self-decomposable distribution D. Finally, we also present the maximum empirical likelihood method specifically for Lévy processes as an alternative to the classical maximum likelihood estimation methodology, when the density function is unknown.
SubjectsStochastic processes, Processos estocàstics
DegreeGRAU EN MATEMÀTIQUES (Pla 2009)
URIhttp://hdl.handle.net/2117/106951
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  • Facultat de Matemàtiques i Estadística - Grau en Matemàtiques (Pla 2009) [282]
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