What is a Markov chain and what is its memoryless property?
A Markov chain is a mathematical system that undergoes transitions from one state to another according to certain probabilistic rules. Its defining characteristic is the memoryless property: the probability of transitioning to any particular state depends solely on the current state and time elapsed, not on the sequence of events that preceded it.
Conditions
- The future state depends only on the present state.
- Transition probabilities are defined between states.
- The system is a Markov chain.
Reasoning, step by step
- Define the Markov chain as a sequence of possible events.
- Identify the memoryless property: future depends only on present, not past.
- Illustrate with a visual animation of a particle moving between nodes in a circular network.
- Explain that this constraint makes the mathematics tractable.
Example
The video shows a circular network of five states ( to ) with a yellow particle moving between them, and states 'where the future depends only on the present, not the past.'
Common misconceptions
- Believing that the memoryless property restricts the model's usefulness or accuracy.
- Assuming that the history of states influences the next transition.
Watch the explanation
2:34 – 3:08Watch this moment ↗
Explore next
Answers are generated from source material and independently checked. Consult the original video or creator if something is unclear.