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Absorbing State

An absorbing state is a state of a Markov chain that cannot be left. For a time-independent stochastic matrix P=(p_(ij)) under the row convention, state i is absorbing iff p_(ii)=1. The other entries in row i are then 0 (Grinstead and Snell 1997, p. 416).

The presence of an absorbing state does not require other states to reach it. That additional reachability condition is part of the definition of an absorbing Markov chain.

See also

Absorbing Markov Chain, Markov Chain

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References

Grinstead, C. M. and Snell, J. L. Introduction to Probability, 2nd rev. ed. Providence, RI: American Mathematical Society, 1997. https://chance.dartmouth.edu/teaching_aids/books_articles/probability_book/Chapter11.pdf.

Cite this as:

Weisstein, Eric W. "Absorbing State." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/AbsorbingState.html

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