Question: Find the correlation function (C(s, t):=mathbb{E}left(X_{S} X_{t}ight), s, t geqslant 0), of the stochastic process (X_{t}:=B_{t}^{2}-t, t geqslant 0), where (left(B_{t}ight)_{t geqslant 0}) is a

Find the correlation function $C(s, t):=\mathbb{E}\left(X_{S} X_{t}ight), s, t \geqslant 0$, of the stochastic process $X_{t}:=B_{t}^{2}-t, t \geqslant 0$, where $\left(B_{t}ight)_{t \geqslant 0}$ is a $\mathrm{BM}^{1}$.

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