Aperiodicity in markov chain - Cross Validated If gcd of these nos =1 then state is aperiodic If gcd not equals 1 (say 'd'), then period equals 'd' For a self loop state it is possible to return to the state in 1,2,3,4 steps Gcd = 1 So the state is certainly aperiodic For non self loop state we find possible no of steps and then find gcd which may be 1 This makes the state
What is the definition of a aperiodic Markov chain? Could we have an aperiodic Markov chain with multiple communication classes where the diagonal of the transition matrix is strictly positive? $\endgroup$ – E Kaufman Commented Jun 17, 2023 at 18:01
aperiodic property and the existence of limiting or stationary . . . And (ii) an irreducible aperiodic Markov chain on a finite state space is recurrent (and hence has a stationary distribution) I do not understand what you mean by self-loop arc If you mean that there is a probability to remain in the same state, this is not correct
Proof and definition aperiodic Markov Chain - Cross Validated Stack Exchange Network Stack Exchange network consists of 183 Q A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers
Intuitive explanation for periodicity in Markov chains A Markov chain is aperiodic if every state is aperiodic My Explanation The term periodicity describes whether something (an event, or here: the visit of a particular state) is happening at a regular time interval
Determining aperiodicity of markov chain - Cross Validated The characterization of aperiodicity given by Exercise 2 8 here basically says a chain is aperiodic if and only if there isn't a capturing state This is a moot point, since I think you can do this much more easily