Question: Give an explicit solution for the mean-reverting rnstein-Uhlenbeck SDE [d X_{t}=alphaleft(mu-X_{t} ight) d t+sigma d B_{t}] with (X_{0}=x).

Give an explicit solution for the mean-reverting Ørnstein-Uhlenbeck SDE

\[d X_{t}=\alpha\left(\mu-X_{t}\right) d t+\sigma d B_{t}\]

with \(X_{0}=x\).

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