ensemble average vs time average

Tags: statistics

Both properties of stochastic process, ensemble average is effectively the expected value, whereas the time average is a strict random variable.

Time average of a stochastic process is simply the average value of a single outcome of a stochastic process.

Modern economics tends to conflate these and use ensemble averages when a time average is probably better.

• https://math.stackexchange.com/questions/1339012/what-does-ensemble-average-mean
• https://www.nii.ac.jp/qis/first-quantum/forStudents/lecture/pdf/noise/chapter1.pdf