Asymptotic expansions in limit theorems for stochastic processes. II

. For a certain class of families of stochastic processes η^ε(t), 0≤t≤T, constructed starting from sums of independent random variables, limit theorems for expectations of functionals F(η^ε0,T]) are proved of the form where w ₀ is a Wiener process starting from 0, with variance σ² per unit time, A _i are linear differential operators acting on functionals, and m=1 or 2. Some intricate differentiability conditions are imposed on the functional. Received: 12 September 1995 / Revised version: 6 April 1998