Please use this identifier to cite or link to this item: http://hdl.handle.net/2445/121869
Title: Càlcul estocàstic per a semimartingales i temps locals
Author: Torre i Estévez, Víctor de la
Director/Tutor: Sanz, Marta
Keywords: Anàlisi estocàstica
Treballs de fi de grau
Semimartingales (Matemàtica)
Moviment brownià
Integrals estocàstiques
Processos de Lévy
Analyse stochastique
Bachelor's thesis
Semimartingales (Mathematics)
Brownian movements
Stochastic integrals
Lévy processes
Issue Date: 29-Jun-2017
Abstract: [en] We start by defining the stochastic integral with respect continuous semimartingales. We then derive Itô’s formula and we show two important applications of this formula: Lévy’s characterization of Brownian motion and the Burkholder-Davis-Gundy inequalities. We extend Itô’s formula for convex functions by using local times. Finally, we apply the theory of local times to the case of Brownian motion: we proof the classical Trotter theorem and we identify the law of the Brownian local time at level 0.
Note: Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2017, Director: Marta Sanz
URI: http://hdl.handle.net/2445/121869
Appears in Collections:Treballs Finals de Grau (TFG) - Matemàtiques

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