A nonlinear renewal theory
Let T be the first passage time across a nonlinear boundary for a perturbed random walk. The present paper presents approximations of the distribution of the overshoot, E(T) and Var(T). An important tool in the proofs are renewal theorems for first passage times across horizontal levels for nonperturbed random walks with a drift that is smaller than the drift of the original, nonperturbed random walk and results about uniform integrability of powers of the difference of the two first passage time processes.
first passage time across a nonlinear boundary
scientific article; zbMATH DE number 4048804