Discrete Stochastic Processes: Markov Chains and Random Walks

Dynamic real-world systems often involve uncertainty that evolves over discrete time steps or random event arrivals. Mastering discrete stochastic processes allows you to analyze and forecast these systems with mathematical precision. This beginner-friendly course provides a clear, text-based guide through essential probabilistic models. You will start with basic definitions and foundational probability principles before exploring key processes used across science, quantitative analysis, and data modeling. What you will learn: Understand fundamental definitions and key properties of discrete random processes; Master Poisson processes, renewal theory, and arrival time distributions; Analyze Markov chains, transition probabilities, and long-term stationary distributions; Explore random walks, boundary behavior, and path properties; Study branching processes and population growth dynamics; Learn foundational Markov Chain Monte Carlo concepts used in modern algorithmic sampling. The material begins with core terminology and probability concepts before building step-by-step through structured analytical models. Designed specifically for beginners, students, and analysts, this course requires no advanced prior background in stochastic calculus. Start reading today to strengthen your quantitative modeling skills.