Convergence of the fixed point theorem with random parameters

Solving stochastic non-linear dynamical problems represents a formidable task which, in many cases, can be achieved solely through numerical simulation techniques. This is true for high dimensional as well as low dimensional problems. One method to deal with the non-linearity is to use the xed point theorem which gives the convergence conditions of the iterative scheme towards the equilibrium point of the equation. In this paper we look at the particular case where the equilibrium equation depends on a random variable. This case arises for instance in the study of coupled non-linear dynamical systems when structural uncertainties are introduced in the dynamical systems. We give almost sure and Lp convergence conditions for the simulation iterative scheme