What's the difference between a white noise process, IID process and random walk?

Question

Just need some clarification between these concepts.

Is an IID with mean zero white noise process? Also is random walk a summation of white noise process?

Answer 1

I believe white noise is used sometimes to indicate both concepts as needed. I don't think there is a clear definition (I may be wrong)

The huge difference between a IID process and a random walk (take a brownian motion) is the fact that the trajectory of IID are discontinuos. This is a huge handicap if you want to use it to model trajectories of actual particles, or stock prices, for example; you could be at $10$ and with the next realization at $-12$, without any relationship between the values.

Sometimes that is what you want, sometimes it is not; for actual things moving in the real world, you want the increments to be independent (meaning I can go up or down irrespective of the history ) but certainly you don't want to "forget" where you are (if you are at $10$, with the next value you could be at $11$ or $9$ but certainly not $-100$