Asymptotic expansions in limit theorems for stochastic processes. – III

For families of processes with independent increments ηɛ(t), 0≤t≤T, with frequent small jumps, limit theorems for expectations of the functionals F(ηɛ[0, T]) are proved of the form [inline-graphic not available: see fulltext] where diD, are positive numbers, Adi are linear integro-differential or differential operators acting on functionals, and some differentiability conditions are imposed on the functional F. The case of power ‘tails’ of the jump distribution is considered.