EXPECTED NUMBER OF EXCURSIONS ABOVE CURVED BOUNDARY BY A RANDOM-WALK

An asymptotic relation for the expected number of excursions above a boundary g(n) by a random walk Sn, n = 1,2, ‥, N is given in terms of an integral involving g. An integral test is given to determine whether the total excursion time has finite expectation. If some moment assumptions hold then the expectation of the total excursions is finite if and only if [formula omitted]. © 1990, Australian Mathematical Society. All rights reserved.