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On a method for an effective calculation of optimal estimates in problems of a filtration of random processes for certain nonlinear evolution differential equations in a Hilbert space. Part 1
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A. A. Fomin-Shatashvili
Published/Copyright:
December 8, 2008
Abstract
In the first part of this paper it is received the closed general expression which can be considered as algorithm for obvious calculation of an optimum estimation in problems of a filtration of random processes accepting the values in abstract Hilbert spaces. Using a condition of existence of density of Radon–Nikodym's measure generated by random process concerning some Gaussian measure (the optimum filter) it is shown that calculation of conditional mathematical expectation is reduced to calculation of an unconditional population mean on the base of obvious expressions.
Received: 2008-01-22
Published Online: 2008-12-08
Published in Print: 2008-November
© de Gruyter 2008
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- Weak solutions for random nonlinear parabolic equations of nonlocal type
- A simplified version of Cochran's theorem in mixed linear models
- On a method for an effective calculation of optimal estimates in problems of a filtration of random processes for certain nonlinear evolution differential equations in a Hilbert space. Part 1
- A remark on some random fixed points of multivalued SL-random operators satisfying the nonstrict Opial's property and corrigendum to “Random fixed points of multivalued random operators with property (D)”
- Discrete time approximation of BSDEs driven by a Lévy process
- Transforming random operators into random bounded operators
- A remark on probability distributions and characteristic functionals for random functions of sets
Keywords for this article
Filtration;
density;
measure;
measurable function;
σ-algebra;
equivalence of measures
Articles in the same Issue
- Weak solutions for random nonlinear parabolic equations of nonlocal type
- A simplified version of Cochran's theorem in mixed linear models
- On a method for an effective calculation of optimal estimates in problems of a filtration of random processes for certain nonlinear evolution differential equations in a Hilbert space. Part 1
- A remark on some random fixed points of multivalued SL-random operators satisfying the nonstrict Opial's property and corrigendum to “Random fixed points of multivalued random operators with property (D)”
- Discrete time approximation of BSDEs driven by a Lévy process
- Transforming random operators into random bounded operators
- A remark on probability distributions and characteristic functionals for random functions of sets
