This book provides essential theoretical tools for stochastic modeling. This Second Edition includes expanded discussion of the most used models in applications such as Markov chains with discrete-time parameters, hidden Markov chains, Poisson processes, and birth and death processes. The authors have also added new topics, including semi-Markov processes, marked Poisson processes, Hawkes processes, time reversibility and detailed balance in continuous-time Markov chains, and age-dependent branching processes. The book includes updated examples, simulation methods, and applications to complement those presented in the first edition. This book is concise and rigorous, presenting the material in an easily accessible manner that allows readers to learn how to address and solve problems of a stochastic nature.

Liliana Blanco-Castañeda, Dr.rer.nat, is a Full Professor in the Department of Statistics at the National University of Colombia, Bogotá. She earned her M.Sc. degree in Mathematics from Universidad Nacional de Colombia, Bogotá and Dr. rer. nat degree in Mathematics from the Johannes Gutenberg Universität. Her research interests include theory of probability, branching processes, and stochastic processes and its applications.

Viswanathan Arunachalam, Ph.D., is an Associate Professor in the Department of Statistics at Universidad Nacional de Colombia, Bogotá. He earned his Ph.D. in Mathematics from the Indian Institute of Technology Madras. He also had positions at Universidad de los Andes, Bogotá and visiting positions at Arizona State University. His research interests include stochastic processes and its applications in biology, reliability and queuing theory, and statistics of financial markets.