I have searched for some posts on math stack exchange, but I do not find a clear answer, can I have an explicit optimal constant for the BDG inequality $$\mathbb{E}\left[\int^T_0 \big|X(s)\big|^2ds\right]^{p/2} \leq C_p\mathbb{E}\left[\sup_{\tau\in [0,T]}\left|\int^\tau_0 X(s) dW_s \right|^p\right]?$$ In my case, I look for $C_p$ for $p=4$.
2026-03-30 06:29:11.1774852151
The optimal constant for Burkholder-Davis-Gundy inequality
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