Numerical methods for SDEs with small noise

In the general case many difficulties arise with realizing numerical methods for SDEs. But we know (see, e.g., Chaps. 1–2 where, in particular, such specific systems as systems with additive and colored noises are treated) that numerical methods adapted to specific systems can be more efficient and easier than general methods. An important instance of a stochastic system is given by differential equations with small noise, since often fluctuations, which affect a dynamical system, are sufficiently small.