Question: PROBLEM 9. (10 points) Let X(t) be a Brownian motion. (a) Use Ito's formula to compute the stochastic integral ( *2+ X (s)?dX (s). (b)

PROBLEM 9. (10 points) Let X(t) be a Brownian motion. (a)

Use Ito's formula to compute the stochastic integral ( *2+ X (s)?dX

(s). (b) What stochastic differential equation does the stochastic process e2X(t)+31 satisfy?

PROBLEM 9. (10 points) Let X(t) be a Brownian motion. (a) Use Ito's formula to compute the stochastic integral ( *2+ X (s)?dX (s). (b) What stochastic differential equation does the stochastic process e2X(t)+31 satisfy? (C) Suppose now that y(t) is a differentiable function. What differential equation does the function e2y(t)+34 satisfy? PROBLEM 9. (10 points) Let X(t) be a Brownian motion. (a) Use Ito's formula to compute the stochastic integral ( *2+ X (s)?dX (s). (b) What stochastic differential equation does the stochastic process e2X(t)+31 satisfy? (C) Suppose now that y(t) is a differentiable function. What differential equation does the function e2y(t)+34 satisfy

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