The Feynman-Stratonovich semigroup and stratonovich integral expansions in nonlinear filtering

The Feynman-Stratonovich semigroup and stratonovich integral expansions in nonlinear filtering Representations for the solution of the Zakai equation in terms of multiple Stratonovich integrals are derived. A new semigroup (the Feynman-Stratonovich semigroup) associated with the Zakai equation is introduced and using the relationship between multiple Stratonovich integrals and iterated Stratonovich integrals, a representation for the unnormalized conditional density, u ( t , x ), solely in terms of the initial density and the semigroup, is obtained. In addition, a Fourier seriestype representation for u ( t , x ) is given, where the coefficients in this representation uniquely solve an infinite system of partial differential equations. This representation is then used to obtain approximations for u ( t , x ). An explicit error bound for this approximation, which is of the same order as for the case of multiple Wiener integral representations, is obtained. Applied Mathematics and Optimization Springer Journals

The Feynman-Stratonovich semigroup and stratonovich integral expansions in nonlinear filtering

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Copyright © 1997 by Springer-Verlag New York Inc.
Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Methods
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