Top row: the global coefficients
αₜ and
σₜ (accumulated signal & noise) alongside
the local SDE coefficients f(t) and
g²(t) (instantaneous drift & diffusion). They
describe the same forward process from different
angles.
Bottom: a 1D particle starts at x₀.
The
blue curve shows
xₜ computed via the global formula
xₜ = αₜx₀ + σₜε. The
red dots show
xₜ computed by accumulating local SDE steps. They agree
— two views, one process.