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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-Solé, Marta |
Keywords: | Anàlisi estocàstica Treballs de fi de grau Semimartingales (Matemàtica) Moviment brownià Integrals estocàstiques Processos de Lévy Analyse stochastique Bachelor's theses 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 |
Files in This Item:
File | Description | Size | Format | |
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memoria.pdf | Memòria | 501.4 kB | Adobe PDF | View/Open |
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