Let $X(t)$ be a centred stationary gaussian process on the reals, with differentiable sample paths, with covariance function $r(t)$
Are $X(0)$ and $X'(0)$ independent? Why?
Are they independent only when $r'(0)=0$ ?
2026-03-25 17:39:43.1774460383
Independence of stationary process and it's derivative.
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