Question: Suppose X = (Xt)is a geometric Brownian motion, dXt = Xt dt + Xt dzt. What is the dynamics of the process y = (yt)

Suppose X = (Xt)is a geometric Brownian motion, dXt = μXt dt + σXt dzt.

What is the dynamics of the process y = (yt) defined by yt = (Xt)n?What can you say about the distribution of future values of the y process?

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