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Stochastic equations for linear random functionals and statistical problems. (English) Zbl 1110.60037

Stochastic differential equations in infinite-dimensional spaces are studied and applied to the filtering problem. With this purpose the notion of linear random functionals is recalled and a generalization of the stochastic integral with respect to the cylindrical Wiener process is developed. Then the existence of a solution of stochastic linear and nonlinear evolution equations in infinite-dimensional spaces by the Galerkin and the fixed point methods is studied.

MSC:

60G20 Generalized stochastic processes
60G44 Martingales with continuous parameter
60G35 Signal detection and filtering (aspects of stochastic processes)
46T12 Measure (Gaussian, cylindrical, etc.) and integrals (Feynman, path, Fresnel, etc.) on manifolds
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