# On Lenglart's Theory of Meyer-sigma-fields and El Karoui's Theory of Optimal Stopping

arXiv: https://arxiv.org/abs/1810.08485 · HTML: https://mlsanity.com/paper/1810.08485/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Oct 2018.

## Built on by (most cited first, 1 of 1)

- [Optimal Stopping via Randomized Neural Networks](https://mlsanity.com/paper/2104.13669/) (2021)

## Abstract (arXiv)

We summarize the general results of El Karoui [1981] on optimal stopping problems for processes which are measurable with respect to Meyer-σ-fields. Meyer-σ-fields are due to Lenglart [1980] and include the optional and predictable σ-field as special cases. Novel contributions of our work are path regularity results for Meyer measurable processes and limit results for Meyer-projections. We will also clarify a minor issue in the proof of the optimality result in El Karoui [1981]. These extensions were inspired and needed for the proof of a stochastic representation theorem in Bank and Besslich [2018a]. As an application of this theorem, we provide an alternative approach to optimal stopping in the spirit of Bank and F"ollmer [2003].