When you talk about randomness, stochastics, and noise, everything always seems to be going back to “Brownian motion” and “white noise”. But what exactly are these things?

The problem is that if you ask someone who researches the subject, you most likely get many different definitions at the same time. The reason is because, although there are many equivalent definitions (and terms), every single one only seems to be a small part of the intuition of what this thing actually is. So I am going to state without proof equivalent formulations of $$B(t)$$, which is the same as $$B_{t}$$, which is the same as $$W_{t}$$… READ MORE