Question: Question 1 [14] We are interested in solving the differential equation dXt = [a(Xt t) + ]dt + dWt For some constants a, , .

Question 1 [14] We are interested in solving the differential equation

dXt = [a(Xt t) + ]dt + dWt

For some constants a, , . 1.1 Consider the auxiliary function Yt = e atXt . Write down the differential equation satisfied by Yt .

1.2 Solve the differential equation obtained in 1. To get the solution Yt

1.3 Show therefore that the solution of (1) is given by (2)

Xt = X0e at + t + e at e asdWs t 0 .

1.4 Evaluate the Expected value and the variance of Xt

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