Stable linear conditionally optimal filters and extrapolators for stochastic systems with multiplicative noises

The applied theory of analytical synthesis of linear conditionally optimal filters and extrapolators in linear differential stochastic systems with white multiplicative non-Gaussian noises is presented. Efficient criteria of unique asymptotic stability of conditionally optimal filters and extrapolators are formulated in terms of special positive definite integral forms and unique boundedness of controllability and observability matrices. White noises are assumed to be derivatives of additive and multiplicative non-Gausisan arbitrary stochastic processes with independent increments. An illustrative example is given. Some generalizations are discussed.