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Title: El movimiento browniano como límite del paseo aleatorio: el teorema de Donsker
Author: Pitarch Ferreiro, Marta
Director/Tutor: Sanz-Solé, Marta
Keywords: Moviment brownià
Treballs de fi de grau
Teorema del límit central
Rutes aleatòries (Matemàtica)
Brownian movements
Bachelor's theses
Central limit theorem
Random walks (Mathematics)
Issue Date: 17-Jan-2019
Abstract: [en] Brownian motion is a continuous time stochastic process with no memory, that is, the current state of the process is not influenced by its past. This property is named ”Markov property”. The main purpose of this paper is to obtain a Brownian motion from a discrete time stochastic process named Random Walk. The Random Walk is also a Markov process. To achieve this goal, we are going to study weak convergence on metric spaces and, in particular, on $C$ ([0, 1]). Brownian motion is the obtained as a weak limit of a sequence of linear interpolations of Random Walk normalized in a suitable way. This is Donsker’s theorem (1951).
Note: Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2019, Director: Marta Sanz
Appears in Collections:Treballs Finals de Grau (TFG) - Matemàtiques

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