Representation of Random Variables as Lebesgue Integrals
Probability
2023-08-08 v3
Abstract
We study representations of a random variable 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 .
Cite
@article{arxiv.2209.08629,
title = {Representation of Random Variables as Lebesgue Integrals},
author = {Sara Biagini and Gordan Zitkovic},
journal= {arXiv preprint arXiv:2209.08629},
year = {2023}
}