Stochastic equations for linear random functionals and statistical problems (Q862249)

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.