The assertion is true. Since $f\in C^1[0,1]$, it lies in the <Cameron-Martin space of Wiener measure>. The <Cameron-Martin theorem> says that the translated law is equivalent, and in particular absolutely continuous, with respect to <Wiener measure>. Its <Radon-Nikodym derivative> is
$$
\exp\!\left(\int_0^1f'(s)dB_s-\frac12\int_0^1f'(s)^2ds\right).
$$

Solution

Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 202 / 5 / c / ii / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/iii/paper-202/5/c/ii/solution