Theorem 5.1.1 (Cameron-Martin-Girsanov, [Theorem 38.5, RW89]).label Let $\wien$ be the classical Wiener measure on $C([0, \infty); \real^{d})$ and $\mathcal{V}$ be equivalent to $\wien$. For each $t \ge 0$, let $\bracs{X_t \ge 0}$ be the canonical process, $\mathcal{F}_{t}^{\circ} = \sigma(\bracs{X_s|0 \le s \le t})$, $\bracs{\mathcal{F}_t}$ be its $\wien/\mathcal{V}$-augmentation, then there exists a previsible $\real^{n}$-valued process $\bracs{c_t|t \ge 0}$ such that for each $t \ge 0$,
\[\frac{d \mathcal{V}}{d\wien}\bigg |_{\cf_t}= \exp\braks{\int_0^t c_s dX_s - \frac{1}{2}\int_0^t |c_s|^2ds}\]
and
\[\tilde X_{t} = X_{t} - \int_{0}^{t} c_{s}ds\]
is a Brownian motion under $\mathcal{V}$.
Conversely, for any previsible $\real^{n}$-valued process $\bracs{c_t|t \ge 0}$,
\[\zeta_{t} = \exp\braks{\int_0^t c_sdX_s - \frac{1}{2}\int_0^t |c_s|^2ds}\]
is a uniformly integrable martingale with respect to