What are absorbing states in a Markov chain and what effect do they have on system trajectories?

Conditions

• Transition probability from the state to itself must be exactly 1.
• The system eventually enters an absorbing state if reachable.

Reasoning, step by step

1. Define an absorbing state as one that cannot be left once entered.
2. Identify the mathematical condition: self-transition probability is 1.
3. Observe that other states may have transitions leading into absorbing states.
4. Conclude that absorbing states create irreversible paths for the system.

Example

The video shows a four-state diagram where states 0 and 3 have self-loops with probability 1. The narrator says: 'There are absorbing states. Once entered, they are never left.'

Common misconceptions

• Thinking that absorbing states are temporary resting places.
• Assuming that the system can escape an absorbing state with a small probability.

Watch the explanation

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