Given a (one-dimensional) stochastic process $X_t$ and Wiener process $W_t$, the Itô isometry says that $$ \mathbb{E}\left(\left[\int_0^TX_tdW_t\right]^2\right)=\mathbb{E}\left(\int_{0}^T X_t^2 dt\right). $$ Is there a similar (or different!) trick to computing $$ \mathbb{E}\left(\left[\int_0^TX_tdW_t\right]^n\right), $$ where $n\in\mathbb{Z}_{\geq 3}$?
2026-04-01 17:25:25.1775064325
Higher order versions of Itô isometry
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