Abstract.
For a wide class of local martingales (M t ) there is a default function, which is not identically zero only when (M t ) is strictly local, i.e. not a true martingale. This default in the martingale property allows us to characterize the integrability of functions of sup s≤t M s in terms of the integrability of the function itself. We describe some (paradoxical) mean-decreasing local sub-martingales, and the default functions for Bessel processes and radial Ornstein–Uhlenbeck processes in relation to their first hitting and last exit times.
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Received: 6 August 1996 / Revised version: 27 July 1998
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Elworthy, K., Li, XM. & Yor, M. The importance of strictly local martingales; applications to radial Ornstein–Uhlenbeck processes. Probab Theory Relat Fields 115, 325–355 (1999). https://doi.org/10.1007/s004400050240
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DOI: https://doi.org/10.1007/s004400050240