Constructing Maximal Germ Couplings of Brownian Motions with Drift
Probability
2025-07-03 v1
Abstract
Consider all the possible ways of coupling together two Brownian motions with the same starting position but with different drifts onto the same probability space. It is known that there exist couplings which make these processes agree for some random, positive, maximal initial length of time. Presently, we provide an explicit, elementary construction of such couplings.
Keywords
Cite
@article{arxiv.2309.16922,
title = {Constructing Maximal Germ Couplings of Brownian Motions with Drift},
author = {Sebastian Hummel and Adam Quinn Jaffe},
journal= {arXiv preprint arXiv:2309.16922},
year = {2025}
}
Comments
12 pages, 3 figures