Given the transition matrices below, find all communicating classes and classify all states:
The probabilities don't matter for this exercise, so I'm just going to put ones for non-zero entries, even though I know this is absurd mathematically:
(A)
1 1 0 1
1 0 0 1
1 0 0 0
1 0 1 0
I believe that the communicating classes are {1,2,4} and {3} and all these are ergodic.
(B)
1 1 1 1
0 0 1 1
1 0 1 0
0 0 1 0
I think the communicating classes are {1,3}, {2}, and {4}.
I'm not quite sure, but I believe states 1,3, and 4 are ergodic, and 3 is of period 2.
(C)
1 1 0 0
1 1 0 0
0 0 0 1
0 0 1 1
The communicating classes are {1,2} and {3,4} with {1,2} of period 2 and {3,4} ergodic.
Is this right? I think I have the communicating classes right, but I'm not sure about the state classifications. Thanks in advance for any help.
The probabilities don't matter for this exercise, so I'm just going to put ones for non-zero entries, even though I know this is absurd mathematically:
(A)
1 1 0 1
1 0 0 1
1 0 0 0
1 0 1 0
I believe that the communicating classes are {1,2,4} and {3} and all these are ergodic.
(B)
1 1 1 1
0 0 1 1
1 0 1 0
0 0 1 0
I think the communicating classes are {1,3}, {2}, and {4}.
I'm not quite sure, but I believe states 1,3, and 4 are ergodic, and 3 is of period 2.
(C)
1 1 0 0
1 1 0 0
0 0 0 1
0 0 1 1
The communicating classes are {1,2} and {3,4} with {1,2} of period 2 and {3,4} ergodic.
Is this right? I think I have the communicating classes right, but I'm not sure about the state classifications. Thanks in advance for any help.