Overview
The defining feature of a Markov chain is the Markov Property: the future is independent of the past, given the present. It is a 'memoryless' process.
Components
- States: The possible conditions of the system.
- Transition Probabilities: The likelihood of moving from one state to another.
- Transition Matrix: A table summarizing all transition probabilities.
Applications
- Predicting weather patterns.
- Modeling stock market fluctuations.
- Google's PageRank algorithm (modeling a 'random surfer' on the web).
- Early text generation models.