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

Perkins, Edwin

doi:10.1090/S0002-9947-1982-0648092-2

On the construction and distribution of a local martingale with a given absolute value
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Trans. Amer. Math. Soc. 271 (1982), 261-281 Request permission

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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