Moment Convergence of Reciprocals of some First Passage Times

摘要

LetTcbe the first passage time above the levelcin a random walk. When the random walk has a positive drift, there are many studies about the limiting behavior ofETCasc#x2192; #x221e;. However, for driftless random walks,ETcis infinite for every positivecandETcyields little information. To remedy this situation, this paper is devoted to the studies of the quantityE(l/Tc) asc#x2192; #x221e; for random walks with nonnegative drifts. An example is given as an application.