Superpositions and the Continuity of Infinitely Divisible Distributions
(1)~~~~~~~~ I+ x dMx(x) 0. The superposition Y = W(X) also has an infinitely divisible distribution. We have shown in [3] (more general results appear in [3] and [5]) that Y = W(X) has Levy parameters yy = 0, Cay2 = yx' and My(x) = fx JI Jo (27rt) - exp {_-y2/2t} dMx(t) dy, x 0.