Un passeig aleatori: el problema de la ruina del jugador

Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2018, Director: Carles Rovira Escofet[en] This paper deals with the idea of random walks and is divided into three sections. In the first one, the ”Gambler’s”ruin problem is explained: from where it emerged, how it was developed, and some resolutions of the problem. In the next section, we introduce the random walk in one dimension with a view to the problem in the previous section. We’ll see different properties of this random walk and we’ll study the most important concepts. In the last section we’ll focus on the two-dimensional random walk. We’ll see the most important properties and what happens in higher dimensions