Note: This page has been translated by MathWorks. Please click here

To view all translated materals including this page, select Japan from the country navigator on the bottom of this page.

To view all translated materals including this page, select Japan from the country navigator on the bottom of this page.

Extract Markov subchain

`sc = subchain(mc,states)`

State

is`j`

*reachable*from stateif there is a nonzero probability of moving from`i`

to`i`

in a finite number of steps.`j`

`subchain`

determines reachability by forming the transitive closure of the associated digraph, then enumerating one-step transitions.Subchains are closed under reachability to ensure that the transition matrix of

`sc`

remains stochastic (that is, rows sum to`1`

), with transition probabilities identical to those transition probabilities in`mc.P`

.If you specify a state in a recurrent communicating class, then

`subchain`

extracts the entire communicating class. If you specify a state in a transient communicating class, then`subchain`

extracts the transient class and all classes reachable from the transient class. To extract a unichain, specify a state in each component transient class. See`classify`

.

[1]
Gallager, R.G. *Stochastic Processes: Theory for Applications.* Cambridge, UK: Cambridge University Press, 2013.

[2]
Horn, R. and C. R. Johnson. *Matrix Analysis.* Cambridge, UK: Cambridge University Press, 1985.

Was this topic helpful?