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

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