Constructing Maximal Germ Couplings of Brownian Motions with Drift
Sebastian Hummel, Adam Quinn Jaffe
TL;DR
This paper presents an explicit, elementary method for constructing maximal germ couplings of two Brownian motions with different drifts, ensuring they agree over a random initial time interval.
Contribution
It introduces a new, explicit construction for maximal germ couplings of Brownian motions with drift, improving understanding of their coupling behavior.
Findings
Constructed explicit couplings for Brownian motions with drift.
Demonstrated the couplings agree over a positive initial time.
Provided elementary methods for coupling construction.
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsStochastic processes and statistical mechanics · Stochastic processes and financial applications · Complex Systems and Time Series Analysis