Numerical methods for some nonlinear stochastic differential equations

Here u ∈ Rn, W(t) is an n-dimensional Brownian motion,f:Rn+ν+1→Rn,g:Rn+ν+1→Rn×n,andAq:Rν×[0,T]→Rn×n,where (Aq, ∣q∣ ⩽ 2m) is a family of square matrices whose elements are sufficiently smooth functions on Rν × [0, T] and Dq=D1q1⋯Dνqν, Di=∂∂xi.