The characteristic functions satisfying (2) below are proved to be essentially the semi-stable laws. Auxiliary simultaneous integral equations are studied in Theorems 1, 2, 2' and 3.

It is shown that the property of multivariate linear regression yields a system of partial differential equations (p.d.e.'s) satisfied by the characteristic functions of the component random vectors.

This paper presents an alternative, characteristic function based approach for the Bayesian design of estimators for dynamic linear systems and linear detection problems. For a measurement update, the ...