Cadenas

#install.packages("markovchain")
library(markovchain)

## Warning: package 'markovchain' was built under R version 4.4.3

## Cargando paquete requerido: Matrix

## Package:  markovchain
## Version:  0.10.0
## Date:     2024-11-14 00:00:02 UTC
## BugReport: https://github.com/spedygiorgio/markovchain/issues

#MATRIZ DE TRANSICIONES
P = matrix(c(0.4,0.12,0.12,.6,0.46,.46,0,.42,.42),nrow = 3,byrow = F) 
P

##      [,1] [,2] [,3]
## [1,] 0.40 0.60 0.00
## [2,] 0.12 0.46 0.42
## [3,] 0.12 0.46 0.42

mc = new("markovchain",transitionMatrix=P,states=c("0","1","2"),name="Cadena 1") 
#GRAFO
plot(mc)

DistEst = steadyStates(mc)
DistEst

##              0         1    2
## [1,] 0.1666667 0.4833333 0.35

#Esperanza estacionaria
sum(DistEst*0:2)

## [1] 1.183333

P%*%P

##        [,1]   [,2]   [,3]
## [1,] 0.2320 0.5160 0.2520
## [2,] 0.1536 0.4768 0.3696
## [3,] 0.1536 0.4768 0.3696

P%*%P%*%P

##          [,1]     [,2]     [,3]
## [1,] 0.184960 0.492480 0.322560
## [2,] 0.163008 0.481504 0.355488
## [3,] 0.163008 0.481504 0.355488

P%*%P%*%P%*%P%*%P

##           [,1]      [,2]      [,3]
## [1,] 0.1681009 0.4840504 0.3478487
## [2,] 0.1663798 0.4831899 0.3504303
## [3,] 0.1663798 0.4831899 0.3504303

P%*%P%*%P%*%P%*%P%*%P%*%P%*%P

##           [,1]      [,2]      [,3]
## [1,] 0.1666982 0.4833491 0.3499528
## [2,] 0.1666604 0.4833302 0.3500094
## [3,] 0.1666604 0.4833302 0.3500094

DistEst%*%P

##           [,1]      [,2] [,3]
## [1,] 0.1666667 0.4833333 0.35