Let $X_t=\int_0^te^{W_s}dW_s$ and $Y_t=\int_0^tW_sdX_s$. How to show that $X$ and $Y$ are martingale square integrable? ($W_t$ - Wiener)
It it enough to show that $\mathbb{E}X_t^2<\infty$, $\mathbb{E}Y_t^2<\infty$ ? If yes, is it: $\mathbb{E}X_t^2=\mathbb{E}\int_0^te^{2W_s}dW_s=0$ ??