Question: Consider the following SDE: dX(t) = X(t) dt + dW(t) 1. Describe the long time behavior of the average of the solution to the above

Consider the following SDE: dX(t) = X(t) dt + dW(t) 1. Describe the long time behavior of the average of the solution to the above SDE. (say t ) (5 pts.) 1 2. Determine the variance of the solution to the above SDE. (15 pts.) 3. Determine the distribution of the random process X(t). (10 pts.)

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