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#'Markov chain simulation
#'
#'@description This function generates a Markov chain X(1), ..., X(n) with transition matrix Q,
#' starting from a state eta0 or the uniform distribution on {1,..., r}
#'
#'@param Q transition probability matrix
#'@param n number of simulated vectors
#'@param eta0 initial value in 1,...,r.
#'
#'@return \item{x}{Generated Markov chain}
#'
#'
#'@export
#'
#'
SimMarkovChain<-function(Q,n,eta0){
r = dim(Q)[1] ; p = dim(Q)[2]
x = rep(0,n) ; x0= matrix(0,n,r)
if(nargs()<3){
ind = sample(1:r,1)
}else ind = eta0
for( k in 1:r){
x0[,k] = sample(1:r, size = n, replace = TRUE, prob = Q[k,])
}
for( i in 1:n){
x[i] = x0[i,ind]
ind = x[i]
}
return(x)
}
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