Improved Monte-Carlo method for solving of integral Fredholm's equations of a second kind, with confidence regions in the uniform norm

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