Grinstead-Snell-Probability · Problem 11.2.1
Markov Chains
Mathematics · absorbing-markov-chains
Problem
In Example 11.4, for what values of and do we obtain an absorbing Markov chain?Intuitive explanation
An absorbing Markov chain requires at least one state that, once entered, you can never leave—a state where the probability of staying put is 1. The key insight is to identify which entries in your transition matrix must equal 1 (and all others in that row must be 0) to "trap" the system. You'll need to find the values of and that make this happen while keeping the matrix valid (all rows sum to 1).
Intuitive explanation
An absorbing Markov chain requires at least one state that, once entered, you can never leave—a state where the probability of staying put is 1. The key insight is to identify which entries in your transition matrix must equal 1 (and all others in that row must be 0) to "trap" the system. You'll need to find the values of and that make this happen while keeping the matrix valid (all rows sum to 1).