Question

Find the steady state for the Markov matrix?

A=[
.2 .4 .3
.4 .2 .3
.4 .4 .4]

Then calculate the limit of A^n = (0,20,0) as n->infinity

Answer 1

let p A = p
where p =
[
a
b
c
]

I got the following simplified equations in a, b, and c
by multipying the above

-2a + b + c = 0
a - 2b + c = 0
a + b - 2c = 0

which gave me:
a = 1/3 , b=1/3 , c=1/3

check: a+b+c = 1, YES!

The steady-state vector is [ 1/3 1/3 1/3 ]