Introduction to Stochastic Processes and Random Systems

How do we predict the unpredictable? From financial markets to network traffic, stochastic processes provide the mathematical framework to model systems that evolve randomly over time. This course guides you through the foundational mathematics of random systems, helping you transition from basic probability to analyzing complex, time-dependent random phenomena with confidence. What you'll learn: 1. Understand the fundamental concepts of probability space, random variables, and joint distributions. 2. Analyze discrete and continuous-time Markov chains to model state transitions over time. 3. Explore Poisson processes and renewal theory for modeling arrival times and event occurrences. 4. Apply random walk models to simulate paths in physical, financial, and computational systems. 5. Practice setting up transition matrices and calculating steady-state probabilities. 6. Read and interpret modern applications of stochastic modeling in machine learning and data science. You will start with essential terminology and basic probability definitions before progressing to sequence behaviors, limiting distributions, and practical modeling scenarios. Every concept is explained through clear, step-by-step written explanations and mathematical breakdowns. Designed for beginners in probability theory, data science, or engineering, this text-only course requires no advanced mathematical prerequisites beyond basic algebra. Start reading today to unlock the mathematical tools used to model uncertainty in the modern world.