Stochastic processes (statistics)
Graduate · Math
Syllabus focus
Topics typically covered
Click a topic for the full text and related unit practice.
Graduate Stochastic processes — outline derived from course README sections and typical US statistics syllabi (OpenIntro / standard OER where applicable).
Markov chains
- Discrete-time Markov chains: classification of states — Discrete-time Markov chains: classification of states
- Stationary distributions — Stationary distributions
- Ergodicity — Ergodicity
- Continuous-time Markov chains — Continuous-time Markov chains
- Birth–death and queueing models — Birth–death and queueing models
- MCMC as Markov chains — MCMC as Markov chains
Poisson and renewal processes
- Poisson process: definitions — Poisson process: definitions
- Properties — Properties
- Compound Poisson processes — Compound Poisson processes
- Renewal theory (introduction) — Renewal theory (introduction)
- Martingales: optional stopping (intro) — Martingales: optional stopping (intro)
- Brownian motion — Brownian motion
- Diffusion (overview) — Diffusion (overview)
Applications to statistics
- Hidden Markov models (introduction) — Hidden Markov models (introduction)
- Stochastic differential equations (overview) — Stochastic differential equations (overview)
- Spatial point processes (preview) — Spatial point processes (preview)
- Simulation of stochastic processes — Simulation of stochastic processes
Study units
Each unit includes a study guide, worksheets, review, practice test, and answer key. One unit is free; subscribe for the full class.
- Markov chains
Discrete-time Markov chains: classification of states
Coming soon - Poisson and renewal processes
Poisson process: definitions
Coming soon - Applications to statistics
Hidden Markov models (introduction)
Coming soon
Notes
Graduate Stochastic processes — outline derived from course README sections and typical US statistics syllabi (OpenIntro / standard OER where applicable). Topic outline: `content/topics/graduate/stochastic_processes_stats.json`.