Solution
= Solution
A <semimartingale> is an <adapted process> of the form $X=X_0+M+A$, where $M$ is a <local martingale> and $A$ is an adapted <finite-variation process>. A sequence of processes $X^n$ converges to $X$ in <uniform convergence on compacts in probability>, abbreviated ucp, when for every $T<\infty$ and $\delta>0$,
$$
\mathbb P\!\left(\sup_{0\leq t\leq T}|X_t^n-X_t|>\delta\right)\longrightarrow0.
$$