
264 Modeling and Inverse Problems in the Presence of Uncertainty
in 1957. For the derivation of (7.102), Dostupov and Pugachev firs t observed
that for a given realization z o f Z the system (7.100) is ba sically the crypto-
deterministic system (7 .88), and they then der ived Equation (7.102) through
instantaneous transformation of random vectors.
It is of interest to note that we can employ arguments similar to those in the
proof for Theore m 7 .3.1 to (7.100) to obtain Equation (7.102). This proof was
originally given in 1961 by Kozin [77] and is repeated here for completeness.
PROOF For any fixed t, the joint characteristic function of X(t) ≡
x(t