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

Abstract

In this article we offer some modification of Monte-Carlo method for multiple parametric integral computation and solving of a linear integral Fredholm equation of a second kind (well posed problem). We prove that the rate of convergence of offered method is optimal under natural conditions still in the uniform norm, and construct an asymptotical and non-asymptotical confidence region, again in the uniform norm.