Markov Convergence Theorem

Assumptions for Convergence

A1: Finite states
A2: Fixed transition probabilities
A3: Can eventually get from any one state to any other
A4: Not a simple cycle (not automatic state changes)

Given A1-A4, a Markov process converges to an equilibrium distribution which is unique.

Implications

• The initial state doesn't matter
• History doesn't matter
• Interventions doesn't matter
• Is this the systemic structural property that prevents diets from succeeding?

Things to Remember

• It could take a long time to reach the equilibrium
• The point of intervention is by changing A2, by changing the transition probabilities
• Changing state: temporary; Changing transition probabilities: permanent