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

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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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