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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.