Defining the Wiener process
Which properties turn a random process into Brownian motion?
Goal: see each of the four defining properties in an experiment — and understand why paths are continuous yet nowhere differentiable.
window [0, 1.00] · sd W(ε) = √ε = 1.00
On a fixed axis the cloud shrinks into zero: W₀ = 0 and the path starts without a jump. On the scaled axis it looks the same at every zoom — that is Brownian scaling.