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):

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