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WROCŁAW UNIVERSITY
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TECHNOLOGY

Contents of PMS, Vol. 20, Fasc. 2,
pages 337 - 341
 

A GLOBAL APPROACH TO FIRST PASSAGE TIMES

Lars Larsson-Cohn

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 J 1 and M 1 topologies are examined. One typically has continuity in M , 1 but in J 1 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: -

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