Iterative methods of stochastic approximation for solving non-regular nonlinear operator equations

Iterative methods for solving non-regular nonlinear operator equations in a Hilbert space under random noise are constructed and examined. The methods use the averaging of the input data. It is not assumed that the noise dispersion is known. An iteratively regularized method of order zero for equations with monotone operators and iteratively regularized methods of the Gauss–Newton type for equations with arbitrary smooth operators are used as the basic procedures. It is shown that the generated approximations converge in the mean-square sense to the desired solution or stabilize (again in the mean-square sense) in a small neighborhood of the solution.