Let (left(B_{t}ight)_{t geqslant 0}) be a (mathrm{BM}^{1}). Show that (X_{t}:=left(B_{t}, int_{0}^{t} B_{s} d sight)) is a diffusion

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Let \(\left(B_{t}ight)_{t \geqslant 0}\) be a \(\mathrm{BM}^{1}\). Show that \(X_{t}:=\left(B_{t}, \int_{0}^{t} B_{s} d sight)\) is a diffusion process and determine its generator.

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