stationary: Compute the stationary distribution of a homogeneous Markov chain
Description
A homogeneous, finite state Markov chain that is irreducible and aperiodic converges to a unique stationary distribution, here called \(\delta\).
As it is stationary, this distribution satisfies
\(\delta \Gamma = \delta\), subject to \(\sum_{j=1}^N \delta_j = 1\),
where \(\Gamma\) is the transition probability matrix.
This function solves the linear system of equations above.
Usage
stationary(Gamma, tol = .Machine$double.eps)
Value
Stationary distribution of the Markov chain with the given transition probability matrix
Arguments
Gamma
Transition probability matrix of dimension c(N,N)
tol
The tolerance for detecting linear dependencies in the columns of Gamma. The default is .Machine$double.eps.