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#up and down markov chains
mcUpDown<-new("markovchain", states=c("up","down"),
transitionMatrix=matrix(c(0,1,1,0),nrow=2, byrow=TRUE),name="UpDown")
#gamblers ruin
gamblerRuinMarkovChain<-function(moneyMax, prob=0.5) {
require(matlab)
matr<-zeros(moneyMax+1)
states<-as.character(seq(from=0, to=moneyMax, by=1))
rownames(matr)=states; colnames(matr)=states
matr[1,1]=1;matr[moneyMax+1,moneyMax+1]=1
for(i in 2:moneyMax)
{
matr[i,i-1]=1-prob;matr[i,i+1]=prob
}
out<-new("markovchain",
transitionMatrix=matr,
name=paste("Gambler ruin",moneyMax,"dim",sep=" ")
)
return(out)
}
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