Recurrence and period
Definition taught in Classes, recurrence, and reversibility, part of Stochastic processes
Recurrence and period
| Type | Definition |
| Taught in | Classes, recurrence, and reversibility |
| Part | Stochastic processes |
State i is recurrent when \mathbb{P}_i(T_i^+<\infty)=1, and transient otherwise. A recurrent state is positive recurrent when \mathbb{E}_i T_i^+<\infty, and null recurrent when the return time is almost surely finite and has infinite mean. The period of i is
d(i)=\gcd\{n\ge 1: p_{ii}^{(n)}>0\}.
Period 1 means aperiodic.
Used in
- Taught in Classes, recurrence, and reversibility, where the derivation and examples are.
- All 3 questions on Classes, recurrence, and reversibility