I have trouble to distinguish these two concepts namely ergodic process and strict-sense stationary process. I look at one of the books about the signal processing that says an ergodic process must be a strict-sense stationary one. So how to show this property?

Can anyone help??

Thanks, Victor

  • 1
    $\begingroup$ What is your understanding of the meaning of ergodicity? Also, this question is closely related to What is the distinction between ergodic and stationary and reading the answers there might help. $\endgroup$ – Dilip Sarwate Dec 3 '13 at 0:11
  • $\begingroup$ I am quite new to this topic, and I think what you said makes senses for me to distinguish both concepts. But I still cannot observe or understand what is the relationship between these two. I think what you meant in the previous post implies erogic process => stationary, while stationary process is not sufficient to guarantee ergodicity, right? $\endgroup$ – user7141 Dec 3 '13 at 0:45
  • $\begingroup$ You still need to tell us what you understand by ergodicity. A few words will suffice; no need for a formal mathematical definition. $\endgroup$ – Dilip Sarwate Dec 3 '13 at 2:47
  • $\begingroup$ I think it should be something like this: The statistics properties can be determined from a long sampled process? Another type of understanding for this, if I understand is correct, no matter where the position for the initial point locates, the system will still reach the steady state or converge in a dynamical system. $\endgroup$ – user7141 Dec 3 '13 at 2:56

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