Contents
How do you determine the periodicity of a Markov chain?
You can show that all states in the same communicating class have the same period. A class is said to be periodic if its states are periodic. Similarly, a class is said to be aperiodic if its states are aperiodic. Finally, a Markov chain is said to be aperiodic if all of its states are aperiodic.
What does period mean in Markov chain?
A state in a discrete-time Markov chain is periodic if the chain can return to the state only at multiples of some integer larger than 1. Periodic behavior complicates the study of the limiting behavior of the chain.
When is a state in a Markov chain periodic?
A state in a discrete-time Markov chain is periodic if the chain can return to the state only at multiples of some integer larger than 1. Periodic behavior complicates the study of the limiting behavior of the chain.
How to write Part 3 of the Markov chain?
Markov Chains (Part 3) Markov Chains – 1 Markov Chains (Part 3) State Classification Markov Chains – 2 State Classification Accessibility • State j is accessible from state i if p ij (n)>0 for some n>= 0, meaning that starting at state i, there is a positive probability of transitioning to state j in somenumber of steps.
How many states are in a Markov chain?
Now imagine that the clock represents a markov chain and every hour mark a state, so we got 12 states. Every state is visted by the hour hand every 12 hours (states) with probability=1, so the greatest common divisor is also 12. So every (hour-)state is periodic with period 12.
What does accessibility mean in a Markov chain?
Markov Chains (Part 3) State Classification Markov Chains – 2 State Classification Accessibility • State j is accessible from state i if p ij (n)>0 for some n>= 0, meaning that starting at state i, there is a positive probability of transitioning to state j in somenumber of steps.