Question: 12. It Calculus (6 marks] (a) Suppose Xt is a Brownian Motion, what is the SDE for the process Y4 = exp(t + 2x)? (b)

12. It Calculus (6 marks] (a) Suppose Xt is a Brownian

12. It Calculus (6 marks] (a) Suppose Xt is a Brownian Motion, what is the SDE for the process Y4 = exp(t + 2x)? (b) Compute (2X+ + 3)dXt, where X is a Brownian Motion. (Hint: Use the integral form of Ito's Lemma] (c) If X, is a Brownian motion, is Y4 = VtX, also a Brownian motion? Why? (Hint: Consider the properties used to define Brownian Motion] 12. It Calculus (6 marks] (a) Suppose Xt is a Brownian Motion, what is the SDE for the process Y4 = exp(t + 2x)? (b) Compute (2X+ + 3)dXt, where X is a Brownian Motion. (Hint: Use the integral form of Ito's Lemma] (c) If X, is a Brownian motion, is Y4 = VtX, also a Brownian motion? Why? (Hint: Consider the properties used to define Brownian Motion]

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