Introduction to Stochastic Processes

Probability stops being about static dice rolls and starts modeling systems that evolve randomly over time — queues building up, stock prices drifting, particles diffusing — and the goal here is to give you the working vocabulary (Markov property, martingales, Lévy processes) to reason about all of them. You'll work through six problem sets that lean heavily on computing conditional distributions and hitting times for the canonical examples (random walks, Poisson processes, Brownian motion), with a written midterm and final testing whether you can wield those tools rather than just recognize them. Building on a solid probability background, this is the bridge course that makes queueing theory, stochastic optimization, and financial engineering electives actually tractable later in the IE curriculum.