A Raikov-Type Theorem for Radial Poisson Distributions: A Proof of Kingman's Conjecture

摘要

In the present paper we prove the following conjecture in Kingman, J.F.C.,Random walks with spherical symmetry, Acta Math.,109, (1963), 11-53. concerninga famous Raikov's theorem of decomposition of Poisson random variables: "If a radial sum of two independent random variables X and Y is radialPoisson, then each of them must be radial Poisson."