stationary {LaMa}

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)

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.

Value

Stationary distribution of the Markov chain with the given transition probability matrix

Examples

Gamma = tpm(c(rep(-2,3), rep(-3,3)))
delta = stationary(Gamma)