Iterative Determination of Distributions by the Monte Carlo Method in Problems with an External Source

In the Monte Carlo (MC) method statistical noise is usually present. Statistical noise may become dominant in the calculation of a distribution, usually by iteration, but is less Important in calculating integrals. The subject of the present work is the role of statistical noise in iterations involving stochastic simulation (MC method). Convergence is checked by comparing two consecutive solutions in the iteration. The statistical noise may randomize or pervert the convergence. We study the probability of the convergence, and the correct estimation of the variance in a simplified model problem. We study the statistical properties of the solution to a deterministic problem with a stochastic source obtained from a stochastic calculation. There are iteration strategies resulting in non-convergence, or randomly stopped iteration.