Applied Probability Lent 2025 syllabus

Below is the range of topics covered in the course; it may change from year to year.

Syllabus:

Basic Aspects of Continuous Time Markov Chains: Markov Property, Regular Jump Chain, Holding Times, Poisson Process, Birth Process, Construction of Continuous Time Markov Chains, Kolmogorov’s Forward and Backward Equations, Non-minimal Chains.
Qualitative Properties of Continuous Time Markov Chains: Class Structure, Hitting Times, Recurrence and Transience, Invariant Distributions, Convergence to Equilibrium, Reversibility, Ergodic Theorem.
Queueing Theory: Introduction, M/M/1 Queue, M/M/\(\infty\); Queue, Burke’s Theorem, Queues in Tandem, Jackson Networks, Non-Markov Queues (M/G/1 Queue).
Renewal Processes: Introduction, Elementary Renewal Theorem, Size Biased Picking, Equilibrium Theory of Renewal Processes, Renewal-Reward Processes, Example (Alternating Renewal Process, Busy Periods of M/G/1 Queue), Little’s Formula, G/G/1 Queue.
Spatial Poisson Processes: Definition and superposition, Conditioning, Renyi's Theorem.