It is pointed out that the Lesovik theory, in which the scattering sta
tes are made use of as a basis set of functions, does not fulfill the
completeness when the incident electron energy is higher than the scat
tering potential. The incompleteness influences the non-local noise an
d leads to a new contribution which is absent in the Lesovik theory. T
he difference between the local noise and the non-local noise is attri
buted to the real transitions in the sample. It is shown from exact an
alysis that the current through double barrier structures (DBS) is wri
tten in a separate form as the sum of contributions resulting from the
sequential and the resonant tunneling processes. The shot noise is, o
n the other hand, also written as a sum of contributions resulting fro
m the sequential and the resonant tunneling processes in addition to t
he correlation term between the sequential and the resonant tunnel pro
cess. (C) 1998 Elsevier Science Ltd. All rights reserved.