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