Adapted Wasserstein distance between the laws of SDEs

Autor:	Backhoff-Veraguas, Julio, Källblad, Sigrid, Robinson, Benjamin A.
Rok vydání:	2022
Předmět:	Mathematics - Probability 60H10 49Q22 (Primary) 60H35 93E20 (Secondary)
Druh dokumentu:	Working Paper
Popis:	We consider the bicausal optimal transport problem between the laws of scalar time-homogeneous stochastic differential equations, and we establish the optimality of the synchronous coupling between these laws. The proof of this result is based on time-discretisation and reveals a novel connection between the synchronous coupling and the celebrated discrete-time Knothe--Rosenblatt rearrangement. We also prove a result on equality of topologies restricted to a certain subset of laws of continuous-time processes. We complement our main results with examples showing how the optimal coupling may change in path-dependent and multidimensional settings. Comment: Strengthened main results and added examples
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2209.03243 Zobrazit plný text záznamu View this record from Arxiv