Nonlinear renewal theory under growth conditions

The paper concerns renewal theory for processes of the form where is a random walk with positive drift and are perturbations with random and deterministic parts. A result of Hagwood and Woodroofe on the expected sample size is generalized: an additional deterministic perturbation summand with ,, causes an additional summand in the asymptotic expansion, where solves the equation . For the proof corresponding results of Lai-Siegmund type on the asymptotic distribution of the excess over the boundary and of Blackwell type are established.