Zero extension of a scale diffusion coefficient at finite endpoints
= Zero extension of a scale diffusion coefficient at finite endpoints
The diffusion coefficient obtained from a <scale transform for an additive-noise diffusion> need only be defined on an open interval. If it is Lipschitz, its limit at a finite endpoint is zero: a positive limit would bound the derivative $1/h$ of the inverse scale and prevent the inverse from diverging. Extending it by zero beyond finite endpoints therefore preserves global <Lipschitz continuity>.