The continuity assumption on the characteristic function is typically made; any characteristic function satisfies(7) . By Theorem 1 of Zinde-Walsh 2010 then the following system of equations holds in S $^{′}$. Assumption 3 . supp( φ ) ⊇ supp( γ ) = W, where W is a convex set in R d that includes an interior point 0 . The support assumption is necessary to solve for γ. The interior point in the case of characteristic functions is zero with the value of the continuous characteristic function equal to 1 at that point. If the system of equations involves functions with W having an interior point a = 0 consider shifted functions. Theorem 1 Under Assumptions 1-3 if (a) γ is continuously differentiable in W, γ (0) = c γ ( ζ ) = c exp ∫ ζ 0 Σ d k =1 κ $_{k}$( ξ ) dξ$_{k}$, (9) 8 γ · φ = ε$_{1}$ ; (8) γ ′ k · φ = ε$_{2}$$_{k}$, k = 1 , ...d.