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LaMa (version 1.0.0)

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.

Examples

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

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