Let (W=left(W^{1}, ldots, W^{d} ight)) be a (d)-dimensional BM. Is the space of martingales (sum_{i=1}^{d} int_{0}^{t} H_{i}left(W^{i}{

Let \(W=\left(W^{1}, \ldots, W^{d}\right)\) be a \(d\)-dimensional BM. Is the space of martingales \(\sum_{i=1}^{d} \int_{0}^{t} H_{i}\left(W^{i}{ }_{.}\right)_{s} d W_{s}^{i}\) dense in the space of square integrable martingales?