Skip to contents

Compute the stationary distribution of a continuous-time Markov chain

stationary_cont.Rd

A well-behaved continuous-time Markov chain converges to a unique stationary distribution, here called \(\pi\). This distribution satisfies $$\pi Q = 0,$$ subject to \(\sum_{j=1}^N \pi_j = 1\), where \(Q\) is the infinitesimal generator of the Markov chain. This function solves the linear system of equations above for a given generator matrix.

Usage

stationary_cont(Q)

Arguments

Q

infinitesimal generator matrix of dimension c(N,N) or array of such matrices of dimension c(N,N,nTracks) if the stationary distribution should be computed for several matrices at once

Value

either a single stationary distribution of the continuous-time Markov chain (vector of length N) or a matrix of stationary distributions of dimension c(nTracks,N) with one stationary distribution in each row

See also

generator to create a generator matrix

Other stationary distribution functions: stationary(), stationary_p()

Examples

# single matrix
Q = generator(c(-2,-2))
Pi = stationary_cont(Q)
# multiple matrices
Q = array(Q, dim = c(2,2,10))
Pi = stationary_cont(Q)