What does Ergodic mean for Random Processes?

[@Giannis132000]

Thank you for the concise and clear explanation!

[@iain_explains]

Glad it was helpful!

[@eneskosar.r]

excellent explanation, simple and accurate!

[@iain_explains]

Glad it was helpful!

[@mrazzaghpour]

Thanks. After watching this video, I was thinking to find a random process that is stationary, but not ergodic. I guess this is a valuable question. The process I found is a constant function, x(t) = c, in which c is a random variable with a specific PDF. Thank you for your clear and concise videos about basic, but challenging, concepts.

[@iain_explains]

Yes, that's right. Here's another of my videos on exactly that topic: "Are Stationary Random Processes Always Ergodic?" kzbin.info/www/bejne/pZ_bq6horbqEaqc

[@samirbouguerra2626]

Thanks a lot for the clear explanation, your channel is gold

[@iain_explains]

I'm so glad you are finding the videos helpful.

[@zaedabdulwali5592]

Thanks to include some examples

[@iain_explains]

Ergodicity is almost always assumed for a random process, unless there are specific clear reasons why it doesn't hold. Keep an eye out for an upcoming video on the channel that will give an example of when it doesn't hold.

[@mq6605]

Thank you very much Professor, it's a very clear explanation.

[@iain_explains]

I'm glad you liked it.

[@pitmaler4439]

Thank you, I think in a stationary process, you can get different characteristics too when you zoom deep enough in the function e.g. take just the area around a lower minimum. That would produce another mean value. Are there any laws that measurements must be long enough?

[@iain_explains]

This will depend on the autocorrelation of the process. For more on this, see: "What is Autocorrelation?" kzbin.info/www/bejne/noDZdmumqqeNgZY

[@menRbrave7]

What does time and ensemble average means?

[@iain_explains]

"Time average" is the average over time, for a given realisation. "Ensemble average" is the average over the realisations, for a given time.

[@tuyensinhftu3221]

what’s ensemble pdf?

[@iain_explains]

It's the pdf. The word "ensemble" is used to emphasise that the density is across the ensemble of all sample functions ... as opposed to the "time histogram" which is across all time, for a particular sample function.

[@leewilliam3417]

Mmmmm😊