Theoretical / proof-based
Stochastic processes (statistics) · Graduate · Math
Learning objectives from the Stochastic processes (statistics) syllabus, grouped by unit. Click an objective for study materials.
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
Learning objectives
Click an objective for study materials.
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
Definitions and structure
- 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
Proofs and reasoning
- MCMC as Markov chains — MCMC as Markov chains
- Poisson process: definitions — Poisson process: definitions
- Properties — Properties
- Compound Poisson processes — Compound Poisson processes
- Renewal theory (introduction) — Renewal theory (introduction)
Abstraction and generalization
- Martingales: optional stopping (intro) — Martingales: optional stopping (intro)
- Brownian motion — Brownian motion
- Diffusion (overview) — Diffusion (overview)
- Hidden Markov models (introduction) — Hidden Markov models (introduction)
- Stochastic differential equations (overview) — Stochastic differential equations (overview)
Modeling and computation
- Apply discrete-time markov chains: classification of states in engine... — Apply discrete-time markov chains: classification of states in engineering contexts
- Apply stationary distributions in engineering contexts — Apply stationary distributions in engineering contexts
- Apply ergodicity in engineering contexts — Apply ergodicity in engineering contexts
- Apply continuous-time markov chains in engineering contexts — Apply continuous-time markov chains in engineering contexts
- Apply birth–death and queueing models in engineering contexts — Apply birth–death and queueing models in engineering contexts
Data and technology
- Use software to explore stochastic processes problems numerically — Use software to explore stochastic processes problems numerically
- Interpret computational results against analytic predictions — Interpret computational results against analytic predictions
- Build spreadsheets or scripts for routine calculations — Build spreadsheets or scripts for routine calculations
- Visualize functions, fields, or datasets tied to course topics — Visualize functions, fields, or datasets tied to course topics
- Connect course methods to lab, industry, or research workflows — Connect course methods to lab, industry, or research workflows
Problem-solving practice
- MCMC as Markov chains — MCMC as Markov chains
- Poisson process: definitions — Poisson process: definitions
- Properties — Properties
- Compound Poisson processes — Compound Poisson processes
- Renewal theory (introduction) — Renewal theory (introduction)
Multi-Unit Problems
Course-level sets that combine skills across study units (coming soon).
Browse Multi-Unit ProblemsWhat each unit includes
Open a unit below for full materials. Typical resources:
- Study guide
- Exam Strategy
- Common Mistakes
- Worksheets
- Word problems
- Mixed Practice
- Multi-Unit Problems
- Review
- Practice test
- Answer key
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
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$1,162 · Stochastic processes (statistics) · 18 tutoring hrs
Study guides, worksheets, reviews, practice tests, and answer keys for 1 class. 18 tutoring hours (1 hr / week · semester). Bundle discount applied vs buying separately. Pay in full via Zelle.