Wiener process · Lévy–Ciesielski construction
Brownian Bridge Builder
Grow a Brownian path from the outside in: draw the endpoint first, then fill each interval with its bridge midpoint. Every refinement halves the step and shrinks the Gaussian kick by √2.
W(m) = ½[W(s) + W(t)] + σ√(t − s)/4 · Z Z ~ N(0, 1), m = (s + t)/2
王晨希202430074
Points1,0252L + 1
Step Δt0.000977T / 2L
Midpoint σ0.0221σ√(T / 2L+1)
Σ(ΔW)² · path 1—→ σ²T = 1
W(T) · path 1—endpoint draw
How much each level adds
Standard deviation of the Gaussian kick introduced at each level, relative to the endpoint draw σ√T. Select a level to jump to it.
Lkick σvaluepoints
Data table · path 1 at the current level
| index | t | W(t) | ΔW |
|---|