Foundations of Markov Chains and Monte Carlo Simulations

Understanding how random systems evolve is essential for making predictions in finance, science, and technology. This text-only course introduces you to the core principles of probability modeling using discrete-time Markov chains and Monte Carlo simulation techniques. You will transition from understanding basic probability to building and analyzing complex stochastic models. By reading through clear, structured explanations and reviewing step-by-step algorithmic examples, you will gain the confidence to simulate random events and predict future states in dynamic systems. What you will learn: Understand the foundational mathematics of probability, state spaces, and transition matrices; Calculate stationary distributions and analyze long-term behavior in discrete-time systems; Apply Monte Carlo integration techniques to approximate complex mathematical functions; Simulate random walks and queueing models using clear, structured logic; Explore modern applications of Markov Chain Monte Carlo (MCMC) in Bayesian inference and modern data analysis. The course begins with fundamental probability concepts and transition properties before moving into practical simulation methodologies and modern computational applications. This course is designed for beginners, aspiring data analysts, and curious learners looking to understand stochastic processes, with no advanced mathematical background required. Start reading today to master the fundamentals of probabilistic modeling and simulation.