Description: This PhD course provides a rigorous introduction to stochastic processes with emphasis on models and methods used in operations management and operations research. Topics include discrete- and continuous-time Markov chains, Poisson processes, renewal processes, renewal reward theory,martingales, Brownian motion, and applications to queues, inventory, reliability, and service systems. The course develops both the mathematical foundations and the modeling skills needed to analyze systems that evolve randomly over time, including long-run behavior, hitting times, stationary distributions, limit results, and performance measures. The emphasis is on proof techniques, probabilistic reasoning, and research-oriented applications. Students are expected to have a solid background in probability, calculus, and linear algebra.