Prove that, for fixed (t), [A_{t}^{(u)} stackrel{text { law }}{=} int_{0}^{t} e^{2left(u(t-s)+W_{t}-W_{s} ight.} d s:=Y_{t}^{(u)}] and that,

Prove that, for fixed \(t\),

\[A_{t}^{(u)} \stackrel{\text { law }}{=} \int_{0}^{t} e^{2\left(u(t-s)+W_{t}-W_{s}\right.} d s:=Y_{t}^{(u)}\]

and that, as a process

\[d Y_{t}^{(u)}=\left(2(u+1) Y_{t}^{(u)}+1\right) d t+2 Y_{t}^{(u)} d W_{t}\]