Definition 3.2.1 (Lipschitz Coefficient).label Let $\sigma: [0, \infty) \times C([0, \infty); \real^{d}) \to \real^{n}$, then $\sigma$ is Lipschitz if there exists $C \ge 0$ such that for any $\theta, \eta \in C([0, \infty); \real^{d})$,
\[\norm{\sigma(t, \theta) - \sigma(t, \eta)}_{\real^n}\le C\norm{\theta - \eta}_{u, [0, t]}\]