Mean recurrence time — meanRecurrenceTime • markovchain

Computes the expected time to return to a recurrent state in case the Markov chain starts there

meanRecurrenceTime(object)

Arguments

object: the markovchain object

Value

For a Markov chain it outputs is a named vector with the expected time to first return to a state when the chain starts there. States present in the vector are only the recurrent ones. If the matrix is ergodic (i.e. irreducible), then all states are present in the output and order is the same as states order for the Markov chain

References

C. M. Grinstead and J. L. Snell. Introduction to Probability. American Mathematical Soc., 2012.

Author

Ignacio Cordón

Examples

m <- matrix(1 / 10 * c(6,3,1,
                       2,3,5,
                       4,1,5), ncol = 3, byrow = TRUE)
mc <- new("markovchain", states = c("s","c","r"), transitionMatrix = m)
meanRecurrenceTime(mc)
#>        s        c        r 
#> 2.266667 4.250000 3.090909