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Conditions for uniform asymptotic stability in the large of the optimal minimum mean-square error linear filter are developed for linear systems whose observations are corrupted by white multiplicative noise in addition to white additive noise. Both discrete-time as well as continuous-time systems are considered. The multiplicative noise model may be useful in problems associated with phenomena such as fading, or reflection of the transmitted signal from the ionosphere, and also certain situations involving sampling, gating, or amplitude modulation. Conditions for existence, uniqueness, and stability of the steady-state optimal filter are also considered for time-invariant systems.