Asymptotic expansions in limit theorems for stochastic processes. – III

. For families of processes with independent increments η ɛ ( t ), 0≤ t ≤ T , with frequent small jumps, limit theorems for expectations of the functionals F (η ɛ [0, T ]) are proved of the form where diD , are positive numbers, A di 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.