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The importance of strictly local martingales; applications to radial Ornstein-Uhlenbeck processes
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UNSPECIFIED (1999) The importance of strictly local martingales; applications to radial Ornstein-Uhlenbeck processes. PROBABILITY THEORY AND RELATED FIELDS, 115 (3). pp. 325-355. ISSN 0178-8051.
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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 less than or equal to 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. Mathematics Subject Classtfication (1991): 60G44, 60J60, 60H15.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Journal or Publication Title: | PROBABILITY THEORY AND RELATED FIELDS | ||||
Publisher: | SPRINGER VERLAG | ||||
ISSN: | 0178-8051 | ||||
Official Date: | November 1999 | ||||
Dates: |
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Volume: | 115 | ||||
Number: | 3 | ||||
Number of Pages: | 31 | ||||
Page Range: | pp. 325-355 | ||||
Publication Status: | Published |
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