Definition 3.3.2 (Uniqueness in Distribution).label Let $\sigma: [0, \infty) \times C([0, \infty); \real^{d}) \to L(\real^{d}; \real^{n})$ and $b: [0, \infty) \times C([0, \infty); \real^{d}) \to \real^{n}$ be previsible path functionals, then the SDE
\[X_{t} = X_{0} + \int_{0}^{t} \sigma(s, X) dB_{s} + \int_{0}^{t} b(s, X) ds\]
has uniqueness in law if for any solutions $X$ and $X'$ such that the distributions of $X_{0}$ and $X_{0}'$ are the same, the distributions of $X$ and $X'$ are the same.