Infinite divisibility of multivariate gamma distributions and M - matrices
R.B. Bapat · 1989
Suppose X=(X1,..,Xp)', has the Laplace transform ψ (t) = ∣Ι + VT∣-½, where V is a positive definite matrix and T= diag(t1,..,tp). It is shown that ψ(t) is infinitely divisible if and only if DV-1 D is an M-matrix for some diagonal matrix D with ± 1's along the diagonal.