A GLOBAL APPROACH TO FIRST PASSAGE TIMES
Abstract: First passage times for discrete-time stochastic processes are studied from a global
point of view, in terms of a mapping that takes a numerical sequence to its first passage time
function. The continuity properties of this mapping with respect to Skorohod’s and
topologies are examined. One typically has continuity in but in only under
extra assumptions. The results are applied to random walks and renewal theory.
1991 AMS Mathematics Subject Classification: Primary: -; Secondary: -;
Key words and phrases: -