The vector field b = (b  b d) : ℝd → ℝd is of class C 3 and the matrix a(x) = [a ij(x)] is symmetric  strictly positive and of class C 3  so that it can be written as a(x) = ½σxσ* x  x∈ℝd  for some function σ : ℝd → ℒ(ℝd) of class C 2 (in fact  we can take σ = √a)