MA4704: Stochastic Process

Learning Outcomes

• Probability & process fundamentals: Explained core probability concepts and definitions of stochastic processes.
• DTMC modelling: Formulated discrete-time Markov chains and constructed transition matrices.
• Limit theorems & stationarity: Applied DTMC limit theorems and identified stationary distributions.
• Gambler’s ruin & extinction: Analysed ruin/extinction probabilities in canonical models.
• Poisson processes: Explained properties and solved standard problems; built Poisson models from data.
• CTMC construction: Formulated continuous-time Markov chains and identified generators.
• Queueing primers: Explained queue length/throughput and solved simple waiting-time/queueing problems.
• Brownian motion & martingales: Stated key definitions and properties for applications.
• Mathematical maturity: Wrote clear proofs and mapped theory to diverse applications.

Takeaways

This three-week summer course compressed a wide range of stochastic process theory into an intensive format, which pushed me to build both speed and depth in understanding. I strengthened my ability to reason rigorously about randomness through topics such as Markov chains, Poisson processes, queueing systems, and Brownian motion. Without group projects, the focus was on individual mastery, and I learned to independently construct proofs, identify stationary behaviours, and connect abstract probability theory with real-world dynamic systems. The fast-paced setting also improved my mathematical maturity, training me to approach uncertainty with structure and long-run reasoning.