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arXiv · 2309.16922

Constructing Maximal Germ Couplings of Brownian Motions with Drift

Sebastian Hummel·Adam Quinn Jaffe
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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.

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Sebastian Hummel, Adam Quinn Jaffe. 2023-09-29. Constructing Maximal Germ Couplings of Brownian Motions with Drift. https://doi.org/10.1214/24-ecp592

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