Simulate a finite state space Markov chain
This function simulates a single realisation from a discrete time Markov chain having a finite state space based on a given transition matrix.
The number of states to be sampled from the Markov chain, including the initial state, which will be sampled using
The transition matrix of the Markov chain. This is assumed to be a stochastic matrix, having non-negative elements and rows summing to one, though in fact, the rows will in any case be normalised by the sampling procedure.
A vector representing the probability distribution of the initial state of the Markov chain. If this vector is of length
ts object containing the sampled values from the Markov chain.
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# example for sampling a finite Markov chain P = matrix(c(0.9,0.1,0.2,0.8),ncol=2,byrow=TRUE) pi0 = c(0.5,0.5) samplepath = rfmc(200,P,pi0) plot(samplepath) summary(samplepath) table(samplepath) table(samplepath)/length(samplepath) # empirical distribution # now compute the exact stationary distribution... e = eigen(t(P))$vectors[,1] e/sum(e)
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