Ergodicity of joint process

1. How do you explain ergodicity?
2. What makes a process ergodic?
3. What is ergodicity example?
4. What is ergodicity in time series?

How do you explain ergodicity?

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.

What makes a process ergodic?

A random process for which ensemble averages are identical to time or spatial averages is said to be ergodic. (See Stochastic Process for definitions of averages.) Both types of averaging are acceptable ways of describing a random process.

What is ergodicity example?

In an ergodic scenario, the average outcome of the group is the same as the average outcome of the individual over time. An example of an ergodic systems would be the outcomes of a coin toss (heads/tails). If 100 people flip a coin once or 1 person flips a coin 100 times, you get the same outcome.

What is ergodicity in time series?

In general, the ergodicity of time series refers to the ergodicity of stationary processes, which means that the process averaged over time behaves identical to the process averaged over space.