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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



On the construction and distribution of a local martingale with a given absolute value

Author: Edwin Perkins
Journal: Trans. Amer. Math. Soc. 271 (1982), 261-281
MSC: Primary 60G44; Secondary 03H10
MathSciNet review: 648092
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Abstract: A local martingale is constructed on an appropriate Loeb space whose absolute value equals a given nonnegative local submartingale. Nonstandard analysis is used to reduce the problem to the discrete time setting where the original construction of D. Gilat is fairly simple. This approach has the advantage of allowing explicit computations. In particular, the distribution of the local martingale is described in terms of the Doob-Meyer decomposition of the original local submartingale.

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Keywords: Submartingale, local martingale, nonstandard analysis
Article copyright: © Copyright 1982 American Mathematical Society