# rfmc: Simulate a finite state space Markov chain In smfsb: Stochastic Modelling for Systems Biology

## Description

This function simulates a single realisation from a discrete time Markov chain having a finite state space based on a given transition matrix.

## Usage

 `1` ```rfmc(n,P,pi0) ```

## Arguments

 `n` The number of states to be sampled from the Markov chain, including the initial state, which will be sampled using `pi0`. `P` 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. `pi0` A vector representing the probability distribution of the initial state of the Markov chain. If this vector is of length `r`, then the transition matrix `P` is assumed to be `r x r`. The elements of this vector are assumed to be non-negative and sum to one, though in fact, they will be normalised by the sampling procedure.

## Value

An R `ts` object containing the sampled values from the Markov chain.

## See Also

`rcfmc`, `ts`

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11``` ```# 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) ```

smfsb documentation built on Aug. 30, 2018, 5:04 p.m.