STOCHASTIC AVERAGING PRINCIPLE FOR SYSTEMS WITH PATHWISE UNIQUENESS

An ergodic type averaging assumption is used to phase out the fast mode component of a system of singularly perturbed stochastic differential equations. The weak convergence of the slow mode variables, implied by the tightness condition, is realized as almost everywhere convergence in a modified probability space. The pathwise uniqueness property is used to unify the weak limit of the slow mode with the unique solution of the reduced system.