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A global approach to first passage times

Larsson-Cohn L.

Probability and Mathematical Statistics

2000

Vol. 20, Fasc. 2

337--341

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 J1 and M1 topologies are examined. One typically has continuity in M1, but in J1 only under extra assumptions. The results are applied to random walks and renewal theory.