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2. This question is on solving stochastic differential equations. The state variable X- satisfies the stochastic differential equation dXt = -y (log (X+) - 0) Xtdt + oXtdWt, where the constants 0, o, y > 0. Consider a time T > t. Show that T log Xr = e-7(T-t) log Xt+ (0- 2 ( 1 - e- 7( I-t) ) to e (T-5) dWs. [35 Marks] Using the results t E YsdWs = E 0 0 YsE [dWs] t 2 E YsdWs = E Y-ds 0 0