English

Representation of Random Variables as Lebesgue Integrals

Probability 2023-08-08 v3

Abstract

We study representations of a random variable ξ\xi 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\xi.

Keywords

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}
}
R2 v1 2026-06-28T01:32:38.185Z