Distribution of State Occupancies
Consider process of repeatedly moving from one state to the next, choosing each subsequent state according to P
- 1? 2 ? 2 ? 1 ? 3 ? 2 ? 2 ? 3 ? 3 ? 1 ? 2 ? 3 ? etc.
Histogram the occupancy number for each state
- n1 = 3 p1 = 0.33
- n2 = 5 p2 = 0.42
- n3 = 4 p3 = 0.25
After very many steps, a limiting distribution emerges
Click here for an applet that demonstrates a Markov process and its approach to a limiting distribution