Is the output of function of two ergodic processes ergodic?

1. How do you know if a process is ergodic?
2. What is an ergodic function?
3. Are all ergodic processes stationary?
4. Is an iid sequence ergodic?

How do you know if a process is ergodic?

A random process is said to be ergodic if the time averages of the process tend to the appropriate ensemble averages. This definition implies that with probability 1, any ensemble average of X(t) can be determined from a single sample function of X(t).

What is an ergodic function?

In mathematics, ergodicity expresses the idea that a point of a moving system, either a dynamical system or a stochastic process, will eventually visit all parts of the space that the system moves in, in a uniform and random sense.

Are all ergodic processes stationary?

So the process is ergodic. However, the variance of any individual sample function shows the original square wave dependence on time, so the process is not stationary. This particular example is wide-sense stationary, but one can concoct related examples that are still ergodic but not even wide-sense stationary.

Is an iid sequence ergodic?

Example 307 (IID Sequences, Strong Law of Large Numbers) Every IID sequence is ergodic. This is because the Kolmogorov 0-1 law states that every tail event has either probability 0 or 1, and (exercise!) every invariant event is a tail event.