Asymptotic expansions in the central limit theorem in Hilbert space (Q1060485)

The author shows that Edgeworth expansions hold for the expectation of differentiable functions of Hilbert space valued sums of i.i.d. random vectors provided the function is bounded by a polynomial of order p, the p-th absolute moment exists and the derivatives are bounded by an exponential function of the norm. The latter condition improves upon previous results of other authors. The results are applied for the expansion of the characteristic function of a quadratic form on Hilbert space.