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How does the transition matrix change in an absorbing Markov chain?

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In an absorbing Markov chain, the transition matrix undergoes a specific structure change to reflect the presence of absorbing states—states that, once entered, cannot be left. The rows corresponding to these absorbing states become part of the identity matrix, with a probability of 1 for remaining in the same state. The remaining rows, associated with transient states, are divided into submatrices: Q, representing transitions among transient states, and R, showing transitions from transient to absorbing states. This structured arrangement highlights the system's dynamics, where transient states gradually transition toward absorption over time.

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