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Brownian motion: a random walk approximation

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hdl:2117/121049

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Gutiérrez Moya, Sergio
Tutor / directorSerra Albó, OriolMés informacióMés informacióMés informació
Document typeBachelor thesis
Date2018-07
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
Brownian motion is one of the most used stochastic models in applications to financial mathematics, communications, engineeering, physics and other areas. Many of the central results in the theory are obtained directly from its definition as a continuous process. As a mathematical object, Brownian motion also have some special and important properties that make it fundamental to understand related mathematical fields and state-of-the-art concepts. The purpose of this work is to review a relatively recent approach which allows to reobtain these results via a random walks approximation. The applications of this particular approach include the local time of Brownian motion and the Black-Scholes model in financial mathematics.
SubjectsProbabilities, Probabilitats
DegreeGRAU EN MATEMÀTIQUES (Pla 2009)
URIhttp://hdl.handle.net/2117/121049
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  • Facultat de Matemàtiques i Estadística - Grau en Matemàtiques (Pla 2009) [318]
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