Just a simple question when we have $v_{st} = \operatorname{cov}(B_s, B_t\mid Z)$, where $B_t$ is a brownian motion. I know that the answer is $\min(s, t) - E[B_s Z]E[B_t Z]/E[Z^2]$ but i don't know how it is obtained. I don't know if it's ok: $v_{st} = E[(B_s - E[B_s\mid Z])(B_t - E[B_t\mid Z])\mid Z]$.
2026-04-13 12:54:20.1776084860
Conditional covariance
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