# Funktion zur Berechnung von Matrizen-Potenzen

matrix.power <- function(mat, pow=2)
  {
  mhelp <- mat
  for(i in 2:pow)
    mhelp <- mhelp%*%mat
  return(mhelp)
  }

# ergodische MK

P <- matrix(c(0.2,0.8,0,0.6,0.4,0,0.2,0.3,0.5), nrow=3, ncol=3, byrow=T)
#P <- matrix(c(0.2,0.7,0.1,0.6,0.4,0,0.2,0.3,0.5), nrow=3, ncol=3, byrow=T)
P
matrix.power(P,2)
matrix.power(P,3)
matrix.power(P,4)
matrix.power(P,5)
matrix.power(P,10)
matrix.power(P,20)
matrix.power(P,30)

# periodische MK

P <- matrix(c(0,1,0,1,0,0,0.2,0.3,0.5), nrow=3, ncol=3, byrow=T)
P
matrix.power(P,10)
matrix.power(P,20)
matrix.power(P,30)
matrix.power(P,50)

matrix.power(P,50)
matrix.power(P,51)
matrix.power(P,52)
matrix.power(P,53)
matrix.power(P,54)