Consider a Markov chain with three and four states respectiv

Consider a Markov chain with three and four states respectively and transition probability matrices given by

A = {(1/2, 1/2, 0), (1/2, 1/4, 1/4), (0, 1/3, 2/3)}
B = {(1/2, 1/2, 0, 0), (1/2, 1/2, 0, 0), (1/4, 1/4, 1/4, 1/4), (0, 0, 0, 1)}

How many irreducibility classes does the Markov chain has and what are they?

4 consider s Markov chain with three tand four states respectively and transition probability matrices given by 1/2 1/2 o A 1/2 1/4 1/4 0 1/3 2/3 1/2 1/2 0 0 B- 1/2 1/2 0 0 1/4 1/4 1/4 1/4 0 1 How many irreducibility classes does the Markov chain has and what are they? a 40 ENG 656 PM

Solution

Let 1 , 2 , 3 be the states of Markov chain A .

Then class(1) ={1,2}

Class (2) ={1,2,3}

Class (3)= {2,3}

Hence class 1 and class 3 are irreducible classes

Let 1,2,3,4 be the states of markov chain B

Class (1)= {1,2}

Class(2)= {1,2}

class (3)= {3}

Class (4)={4}

Hence all the classes are irreducible