Stationary distributions of a Markov chain

Returns the stationary distributions of a Markov chain: the probability vectors \(\pi\) with \(\pi P = \pi\). There is one for each recurrent class; every stationary distribution is a convex combination of them.

Usage

steadyStates(object)

Arguments

object: A markovchain object.

Value

A matrix with one stationary distribution per row (per column if the chain is stored by columns, byrow = FALSE), with the states as column (row) names.

Note

The steady states are identified starting from which eigenvectors correspond to identity eigenvalues and then normalizing them to sum up to unity. When negative values are found in the matrix, the eigenvalues extraction is performed on the recurrent classes submatrix.

Author

Giorgio Spedicato

Examples

statesNames <- c("a", "b", "c")
markovB <- new("markovchain", states = statesNames, transitionMatrix =
                matrix(c(0.2, 0.5, 0.3, 0, 1, 0, 0.1, 0.8, 0.1), nrow = 3,
                byrow = TRUE, dimnames=list(statesNames,statesNames)),
               name = "A markovchain Object" 
)       
steadyStates(markovB)
#>      a b c
#> [1,] 0 1 0