A Markov chain is said to be aperiodic9 if and only if there exists a specific time t > 1 such that for every pair of states x and x’, we have P(Xt =x’ |X1 =x) > 0. If a Markov chain is aperiodic, it will also be irreducible and, hence, have a unique stationary distribution, say Pr(X). 10 Moreover, if the chain is aperiodic, it will converge to its stationary distribution. That is,
for all states x and x’. Hence, when simulating the Markov chain, the simulated instantiations are eventually sampled from the stationary distribution Pr(X) and become independent of the initial state at time 1.
Consider now the Markov chain for a binary variable X with the transition matrix P(x|x¯) = 1 and P(x¯|x) = 1; hence, P(x¯|x¯) = 0 and P(x|x) = 0. Is this chain aperiodic? Is it irreducible? If it is, identify its unique stationary distribution. Will the chain converge to any distribution?
Delivering a high-quality product at a reasonable price is not enough anymore.
That’s why we have developed 5 beneficial guarantees that will make your experience with our service enjoyable, easy, and safe.
You have to be 100% sure of the quality of your product to give a money-back guarantee. This describes us perfectly. Make sure that this guarantee is totally transparent.Read more
Each paper is composed from scratch, according to your instructions. It is then checked by our plagiarism-detection software. There is no gap where plagiarism could squeeze in.Read more
Thanks to our free revisions, there is no way for you to be unsatisfied. We will work on your paper until you are completely happy with the result.Read more
Your email is safe, as we store it according to international data protection rules. Your bank details are secure, as we use only reliable payment systems.Read more
By sending us your money, you buy the service we provide. Check out our terms and conditions if you prefer business talks to be laid out in official language.Read more