Check whether a Markov chain is irreducible

A Markov chain is irreducible if all its states communicate, i.e. form a single communicating class.

Usage

is.irreducible(object)

Arguments

object: A markovchain object.

Value

TRUE if the chain is irreducible, FALSE otherwise.

Details

Irreducibility does not imply aperiodicity: an irreducible chain on finitely many states has a unique stationary distribution, but it converges to it from every initial state only if it is also aperiodic (see period() and is.regular()).

References

Feres, Matlab listings for Markov Chains.

Author

Giorgio Spedicato

Examples

statesNames <- c("a", "b")
mcA <- new("markovchain", transitionMatrix = matrix(c(0.7,0.3,0.1,0.9),
                                             byrow = TRUE, nrow = 2, 
                                             dimnames = list(statesNames, statesNames)
           ))
is.irreducible(mcA)
#> [1] TRUE