= Strong well-posedness of additive-noise equations with bounded continuous drift
The <zero extension of a scale diffusion coefficient at finite endpoints> makes the transformed equation globally Lipschitz. Inverting its solution gives the original additive-noise equation. The pathwise bound $|X_t|\leq|x|+\sup_{s\leq T}|W_s|+\|b\|_\infty T$ prevents the inverse scale from reaching infinity at any finite time. This proves global strong existence and <pathwise uniqueness> even when the original drift is not Lipschitz.
Back to article page
