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Bachelor thesis

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2017-06-29

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cc-by-nc-nd (c) Vı́ctor de la Torre i Estévez, 2017
Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/121869

Càlcul estocàstic per a semimartingales i temps locals

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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.

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Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2017, Director: Marta Sanz

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Anàlisi estocàstica, Treballs de fi de grau, Semimartingales (Matemàtica), Moviment brownià, Integrals estocàstiques, Processos de Lévy

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Analyse stochastique, Bachelor's theses, Semimartingales (Mathematics), Brownian movements, Stochastic integrals, Lévy processes

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Treballs Finals de Grau (TFG) - Matemàtiques

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TORRE I ESTÉVEZ, Víctor de la. Càlcul estocàstic per a semimartingales i temps locals. [consulted: 9 of October of 2026]. Available at: https://hdl.handle.net/2445/121869

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