Modelos estadísticos para la detección de patrones en medio ambiente y finanzas.

Abstract

In the present work some aspects of probability theory are studied through category theory. To do this, it begins with a review of measure theory and probability theory. Then, the basic concepts of category theory are developed and examples of them are presented in the probabilistic context to illustrate them. Finally, the Prob category of probability spaces is presented, in which the central components of probability theory are reformulated; such as measurability, independence and conditional expectation, on the theoretical constructions of categories.