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Is the Markov chain aperiodic?
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 is the condition of Markov chain is said to be irreducible?
A Markov chain in which every state can be reached from every other state is called an irreducible Markov chain. If a Markov chain is not irreducible, but absorbable, the sequences of microscopic states may be trapped into some independent closed states and never escape from such undesirable states.
What are the properties of a Markov chain?
Properties of Markov Chains: Reducibility. Markov chain has Irreducible property if it has the possibility to transit from one state to another. Periodicity. If a state P has period R if a return to state P has to occur in R multiple ways. Transience and recurrence. Ergodicity.
What is a Markov chain used for?
Markov chains are primarily used to predict the future state of a variable or any object based on its past state.
Markov chains also play an important role in reinforcement learning . Markov chains are also the basis for hidden Markov models, which are an important tool in such diverse fields as telephone networks (which use the Viterbi algorithm for error correction), speech recognition and bioinformatics (such as in rearrangements detection).
How do RNNs differ from Markov chains?
RNNs differ from Markov chains, in that they also look at words previously seen (unlike Markov chains, which just look at the previous word) to make predictions. In every iteration of the RNN, the model stores in its memory the previous words encountered and calculates the probability of the next word.