Recurrence Time

Topics: Markov Chain - Stochastic Process

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(definition)

In the context of a Markov chain, the recurrence time is the minimum amount of steps that are needed to go back to a given state for the first time.

Compare the first-passage time, which refers to the minimum amount of steps that are needed to get to a state (for the first time, too).

The recurrence time to a state $i$, denoted ${\mu }_{ii}$ (similarly to a first-passage time), is given by:

$${\mu }_{ii}=\frac{1}{{\pi }_i}$$

…where ${\pi }_i$ is the steady state probability of $i$.