Aperiodic Markov chain
Topic of Classes, recurrence, and reversibility, part of Stochastic processes
Aperiodic Markov chain
| Type | Topic |
| Taught in | Classes, recurrence, and reversibility |
| Part | Stochastic processes |
| Questions using it | 2 |
The period of a state i is d(i)=\gcd\{n\ge1:p_{ii}^{(n)}>0\}, and the state is aperiodic when d(i)=1. States in one communicating class share a period. A periodic chain can have a stationary law and still never converge to it, as the two-state alternation shows.
In Classes, recurrence, and reversibility
Period 1 means aperiodic.
Used in
- Taught in Classes, recurrence, and reversibility
- Also used in Markov chains · Discrete-time Markov chains · Continuous-time Markov chains · Markov chains, Gibbs sampling, and Metropolis–Hastings
- Questions that use it (2) — The limit of the three-state chain · Any two-state chain (answer)
- All 3 questions on Classes, recurrence, and reversibility
See also
Communicating classes · Finite irreducible chains · Irreducible Markov chain · Limiting distribution · Recurrence and period · Detailed balance · Return and period · Global balance and detailed balance