| One of the main objectives of this work is to study the Euler-type stochastic difference scheme for systems of stochastic differential equations. By developing a stochastic version of the Taylor formula the mean-square convergence of the approximation scheme is investigated. Under certain stability-type conditions time-invariant error estimates are obtained. Furthermore, an attempt has been made to extend these results to stochastic singularly perturbed systems. In order to study and approximate the slow-state solution, a generalized version of the stochastic averaging principle is introduced. Morover, a step is taken to establish a relationship between the averaging assumption and certain ergodic-type properties of the random process determined by an auxiliary system of stochastic differential equations. |
