Let (left(B_{t}ight)_{t geqslant 0}) be (mathrm{BM}^{1}) and (left(f_{n}ight)_{n geqslant 1}) a sequence in (mathcal{L}_{T}^{2}) such that (f_{n}

Question:

Let $\left(B_{t}ight)_{t \geqslant 0}$ be $\mathrm{BM}^{1}$ and $\left(f_{n}ight)_{n \geqslant 1}$ a sequence in $\mathcal{L}_{T}^{2}$ such that $f_{n} ightarrow f$ in $L^{2}\left(\lambda_{T} \otimes \mathbb{P}ight)$. Then $f_{n} \bullet B ightarrow f \bullet B$ in $\mathcal{M}_{T}^{2, c}$.

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