The <Itô isometry> for the elementary predictable integrand in $M^{(n)}$ gives
$$
\mathbb E(M_t^{(n)})^2
=4\mathbb E\sum_kX_{t_{k-1}^n}^2
 (X_{t\wedge t_k^n}-X_{t\wedge t_{k-1}^n})^2
\leq4C^2\mathbb EA_t^{(n)}\leq4C^4.
$$

Solution

Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 202 / 2 / a / ii / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2025/iii/paper-202/2/a/ii/solution