. Let an OUP satisfy the SDE dX =(p — X)dt adW, with X(0) = x.

Show that the transformed process Y = e‘X satisfies dY = e\pdt ad W).

Hence 284 Diffusion processes Y(t)= F(0) + /i dt' -f a Jo e^'dWia Now determine the mean and variance of Y(t) using (12.24) and (12.25).

Hence verify the formulae for the mean and variance of the OUP given in the text and the expression in section 12.4 for the transition density of an OUP.