Question: Problem 8 (10 points). Let {W}to be a standard Wiener process, and U : R - R, o : R - R and y :

Problem 8 (10 points). Let {W}to be a standard Wiener process, and U : R - R, o : R - R and y : R -> R be functions that are sufficiently regular. Assume further that y is invertible. Show that {X}tzo is a strong solution to dXt = u(Xt) dt + o(X) dWt, t20 if and only if Yt := v(Xt) is a strong solution to -1 ( Yt) 2 1 (T ) dyt = 0(1-1 (Y+) ) expl - 02 (T ) drdWt, t20

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