Method Monte-Carlo for solving of non-linear integral equations

Abstract

We offer in this short report a simple Monte-Carlo method for solving a well-posed non-linear integral equations of second Fredholm's and Volterra's type and built a confidence region for solution in an uniform norm, applying the grounded Central Limit Theorem in the Banach space of continuous functions. We prove that the rate of convergence our method coincides with the classical one

References in corpus (5)

• Relations between exponential tails, moments and moment generating functions for random variables and vectors
• Vector rearrangement invariant banach spaces of random variables with exponential decreasing tails of distributions
• Monte-Carlo method for multiple parametric integrals calculation and solving of linear integral Fredholm equations of a second kind, with confidence regions in uniform norm
• A simple Monte Carlo method for solving of Navier-Stokes Equations
• Existence and smoothness of the solution to the Navier-Stokes