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2865概率困难derivationmedium

A Stable Law with No MGF

题目

Suppose X1,X2,X_1,X_2,\dots are i.i.d. with characteristic function \[ \phi_X(u)=\exp(-c|u|^{3/2}),\qquad c>0. \] Show that \[ n^{-2/3}(X_1+\cdots+X_n) \] has the same distribution as X1X_1.

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