Markov chains: period of a state

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SUMMARY

The discussion focuses on understanding the concept of periodicity in Markov chains, specifically the period of a state. The user inquires about a state that can return in steps of 3, 5, 7, 9, and 11, leading to the conclusion that the greatest common divisor (gcd) of these steps is 1, indicating that the state is aperiodic. The conversation references the definition of periodicity and gcd in the context of Markov chains, clarifying that if the gcd is k, the state returns at intervals of k, 2k, etc. Additional resources, such as Wikipedia and a Stack Exchange link, are provided for further explanation.

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  • Understanding of Markov chains and their properties
  • Knowledge of greatest common divisor (gcd) in mathematics
  • Familiarity with periodicity concepts in stochastic processes
  • Basic statistics terminology and notation
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  • Study the definition and properties of Markov chains
  • Learn about the implications of periodicity in Markov processes
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mmarkov
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Hello,

I am trying to understand the intuition of the definition of the period of a state in a Markov chain.

Say for example we can go from state i to state i in 3,5,7,9,11... and so on steps.
The gcd here is one. So is this aperiodic state or one with periodicity of 2.

Thanks
 
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