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.
Acknowledgments
The authors would like to thank Fausto Gozzi for suggesting some related literature. They are also grateful to the anonymous referees, and the Editors for a number of constructive comments that improved the quality of this paper.
Citation
Sara Biagini. Gordan Žitković. "Representation of random variables as Lebesgue integrals." Bernoulli 30 (3) 1878 - 1893, August 2024. https://doi.org/10.3150/23-BEJ1656
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