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I have a question in quantitaitive finance. Please provivide all calculation steps. 6.0rnstein-Uhlenbeck Process. Suppose that X follows an Ornstein-Uhlenbeck process, clXt = - xt)dt

I have a question in quantitaitive finance. Please provivide all calculation steps.

6.0rnstein-Uhlenbeck Process. Suppose that X follows an Ornstein-Uhlenbeck process, clXt = - xt)dt + dWt, xo = r, > O. a) Show that the solution is given by Xt = eKtn + _ eKt) + (3e Kt eKSdWs b) Find the limiting mean and the variance of Xt as t goes to oc.

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