Are Stationary Random Processes Always Ergodic?

Explains the how Stationarity is related to Ergodicity in random processes, using an example and diagrams.

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[otiebrown]

My opinion?
With good judgment, most of them are.
I used Ergodic data to predict the tracking accuracy of the human eye - with good results, when calculating Time Series data.

[Yilin-wkgl]

Hi professor, I wonder if you do some research on the random field? And could you give me some suggestions on learning the 2D random field, like some textbooks or whatever?

[ssgg]

Hi Iain, great videos! I'm confused about one point. At each time point "t" we have a pdf describing the random variable "x(t)". For a stationary process this pdf is the same for all "t". I hope this is correct so far.

In this example our stationary pdf has a bimodal distribution with Gaussians at 20k and 30k feet. And yet each sample realization (each aircraft) is obviously not sampling from that entire pdf: it is sampling from just one of those Gaussians at either 20k or 30k feet. Although this makes sense in reality, it feels like there's something missing in our description of the random process model if each realization is not actually drawing from the entirety of our stationary pdf (which describes x(t) across all possible realizations).

Does my question make sense? Basically, how can we have a stationary random process, but each realization can draw from only part of that pdf, resulting in a non-ergodic process?

[ashutoshsingh-etvm]

Hello, sir I have one doubt when I use FFT by folding and found total energy in frequency and time domain, respectively it's coming twice, but it should be the same, I guess. Can you tell me why this is happening?

[DamaKubu]

I like your simple intuitive explanation, but there are at least two types of stationarity.

What you mean here is refering to stationary in wide sense? That is the mean and variance of distribution not changing.

[Hassan_MM.]

Stationarity : Their Marginal or Joint prob.functions are time independent
Ergodicity : Their probability function is Time independent. Specifically, pattern or type of their Randomness doesn't change over Time
Is it so ❗️

[gingarrison]

Hi professor, I want to know why the Topic of "random" is important for telecommunications

[yuho]

Hi professor, I sent an email to your gmail about some questions. Please help answer, thx