We study representations of a random variable ξ as an integral of an adapted process with respect to the Lebesgue measure. The existence of such representations in two different regularity classes is characterized in terms of the quadratic variation of (local) martingales closed by ξ.

Representation of random variables as Lebesgue integrals / Biagini, Sara; Zitkovic, Gordan. - In: BERNOULLI. - ISSN 1573-9759. - 30:3(2024), pp. 1878-1893. [10.3150/23-BEJ1656]

Representation of random variables as Lebesgue integrals

Sara Biagini
;
2024

Abstract

We study representations of a random variable ξ as an integral of an adapted process with respect to the Lebesgue measure. The existence of such representations in two different regularity classes is characterized in terms of the quadratic variation of (local) martingales closed by ξ.
2024
Absolutely continuous representation , Girsanov theorem , Martingale representation , Quadratic Variation
Representation of random variables as Lebesgue integrals / Biagini, Sara; Zitkovic, Gordan. - In: BERNOULLI. - ISSN 1573-9759. - 30:3(2024), pp. 1878-1893. [10.3150/23-BEJ1656]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11385/234438
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