  This document presents a compilation of results related to the theory of
stochastic processes, with a specific focus on Markov processes, regenerative
processes, renewal processes, and stationary processes. The relevance of these
topics lies in the ability to identify regeneration points and the necessary
conditions to ensure the stationarity of the process. The study begins with a
review of Markov chains and continues with the analysis of processes that
satisfy the strong Markov property. Subsequently, it delves into renewal
processes, regenerative processes, and finally, stationary regenerative
processes, highlighting the results presented by Thorisson [22]. This work is
not intended to be exhaustive but aims to provide a solid foundation for
further deepening the knowledge of these processes, given their broad range of
applications in cryptography [16], queueing theory [15], and Monte Carlo
methods [23]. Additionally, the importance of Poisson-type processes is
emphasized due to their numerous applications (see [8]).
