Topología de Skorohod y algunas aplicaciones

Abstract

The time series, which are pathways associated with certain stochastic processes, represent a very important role in trying to forecast some weather events, financial events, medical events, such as: oil prices, sales of a company, the variation interest rates, heart rate, among others. In this context, it is necessary to analyze the probabilistic background that time series have, their topology and the different processes that generate. This study summarizes existing definitions and key results, and organizes a sequence between the theory of Skorhod's space (D, D), stochastic processes and their applications. It is in our interest to understand the theoric link of space D with stochastic processes (càdlàg). To simulate some stochastic processes will allow us to understand the behavior and involvement of the theorems and propositions presented. Finally, we try to put it into practice through an application, which is simple but contains the substance of the exposed theory.