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.
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