PeriodicChain.md (680B)
1 # Periodic (Markov) Chain 2 3 L17 4 5 **Definition:** Periodic Markov chains are a specific type of Markov chain defined as a chain with groups such that all transitions frome one group lead to the next group. 6 7 Periodic Markov chains are interesting because they never achieve a steady state. 8 9 Example: 10 11 Imagine you are walking in circles at a constant rate. You start at location 0. The next time you are polled you are at location 1 then location 2 then 0 again. This cycle repeats ad infinium. 12 13 Each transition in the above example has a probability of 1 and the current state will always n mod 2 where n is the number of steps since the intial state assuming the intial state is 0.