Exercise 7.7 Consider the random variable

where Z1, Z2, . . . are independent and identically distributed standard Gaussian variables. Show that the law of X is infinitely divisible. If Y is a L´evy process with Y (1) = X, find a representation for Y (t), for any t > 0. Does Y have a Brownian component?

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IM 8 (2k-1)2