  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.
