- 55

- 0

**1. Homework Statement**

Transition matrix is

0 0 1

0 0 1

(1/3) (2/3) 0

"argue that this chain is aperiodic"

**2. Homework Equations**

definition of aperiodicity - there must exist a time n such that there is a non-zero probability of going from state i to state j for all i & j

**3. The Attempt at a Solution**

This definition doesn't seem to hold for my chain ... for example, to go from state 1 to state 2 n has to be odd.. but to go from state 1 to state 1 or 3 n has to be even..

Am I just getting this definition muddled up? Could someone elaborate on it for me? Thanks