An introduction to random variables, random vectors and stochastic processes

Abstract

This book is aimed at covering the bases on random variables, random vectors and stochastic processes, necessary to be able to address the study of stochastic models based mainly on random and stochastic differential equations. The approach of the text is fundamentally practical. The theoretical results, including demonstrations of a more constructive nature, are combined with numerous examples and exercises chosen with the aim of instructing in fundamental ideas and interpretations. At the end of each chapter two appendices have been included. The first appendix contains a collection of carefully chosen problems for the reader to work on the main contents of the chapter, and also to study, through the proposed problems, some theoretical extensions that have not been dealt with throughout the corresponding chapter. Therefore, solving these proposed exercises is an excellent opportunity to go beyond the contents developed in each chapter. In the second appendix, we have included the resolution of some exercises using the Mathematicar software.These exercises have been selected just to illustrate how to carry out basic computations