Learning Notes

Stochastic – Ergodic Process

Definition

A stochastic process is ergodic if the time average equals to the ensemble average.

For discrete time process (random walk):

\displaystyle \text{exp}[X(t)] = \frac{1}{T} \sum_{t\in T} X(t)

For continuous time process (random flight):

\displaystyle \text{exp}[X(t)] = \frac{1}{T} \int_{T} X(t) dt

See Also

Stochastic Process
Stationary Process ā€“ Stochastic

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