In this program
Discrete-time processes
Stochastic processes · Standard syllabus
Markov chains
Objectives
- Markov chains
- Stationary distributions
- Martingales
- Optional stopping
- Doob's martingale convergence theorem (statement)
- Martingale inequalities
- Burkholder (introduction)
- Random walks
Study materials
- Study guideComing soon
- Exam StrategyComing soon
- Common MistakesComing soon
- WorksheetsComing soon
- Word problemsComing soon
- Mixed PracticeComing soon
- Multi-Unit ProblemsComing soon
- ReviewComing soon
- Practice testComing soon
- Answer keyComing soon
Interactive practice
Quizzes, typed answers, and flashcards for this unit — coming soon.
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Quiz
Multiple-choice questions with instant feedback
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Typed practice
Type answers and check them
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Flashcards
Vocabulary and key facts
- Coming soon
Mixed quiz
Harder mixed review for this standard