Identity Markov chain

Builds the Markov chain whose transition matrix is the identity: every state is absorbing, so the chain never moves.

Usage

identityChain(n, states = NULL, name = "Identity chain")

Arguments

n

The number of states. It can be omitted when states is given.

states

An optional character vector of n state names. Defaults to as.character(1:n).

name

The name slot of the result.

Value

A markovchain object with n states.

Details

The chain is the neutral element of the product of transition matrices (identityChain(n) * mc equals mc for a chain mc on the same states) and the extreme case of lazyChain. Every state is its own closed class, so every distribution is stationary.

See also

randomMarkovChain, lazyChain

Examples

identityChain(3)
#> Identity chain 
#>  A  3 - dimensional discrete Markov Chain defined by the following states: 
#>  1, 2, 3 
#>  The transition matrix  (by rows)  is defined as follows: 
#>   1 2 3
#> 1 1 0 0
#> 2 0 1 0
#> 3 0 0 1
#> 
identityChain(states = c("a", "b"))
#> Identity chain 
#>  A  2 - dimensional discrete Markov Chain defined by the following states: 
#>  a, b 
#>  The transition matrix  (by rows)  is defined as follows: 
#>   a b
#> a 1 0
#> b 0 1
#> 
absorbingStates(identityChain(3))
#> [1] "1" "2" "3"