First passage time distribution of a set of states

Distribution of the first passage time into a set of states: the probability that a Markov chain started in state enters set for the first time at step \(k = 1, \dots, n\).

Usage

firstPassageMultiple(object, state, set, n)

Arguments

object

A markovchain object.

state

Name of the initial state.

set

Names of the states of the target set.

n

Number of steps, a positive integer.

Value

A one-column matrix (column "set") with n rows: row \(k\) is the probability that the first passage into set happens at step \(k\).

References

Feres, R. Notes for Math 450: Matlab listings for Markov chains. Washington University in St. Louis.

Gallager, R. G. 6.262 Discrete Stochastic Processes, course notes, chapter 5. MIT OpenCourseWare.

See also

Other first passage and hitting: absorptionProbabilities(), committorAB(), firstPassage(), hittingProbabilities(), meanAbsorptionTime(), meanFirstPassageTime(), meanNumVisits(), meanRecurrenceTime(), noofVisitsDist()

Author

Vandit Jain

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)))
firstPassageMultiple(markovB, "a", c("b", "c"), 4)
#>      set
#> 1 0.8000
#> 2 0.4000
#> 3 0.1190
#> 4 0.0379