English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

In classical optimal transport, the contributions of Benamou$-$Brenier andMcCann regarding the time-dependent version of the problem are cornerstones ofthe field and form the basis for a variety of applications in othermathematical areas.  In this article, we characterize solutions to the martingaleBenamou$-$Brenier problem as $\textit{Bass martingales}$, i.e. transformationsof Brownian motion through the gradient of a convex function. Our result isbased on a new (static) Brenier-type theorem for a particular weak martingaleoptimal transport problem. As in the classical case, the structure of theprimal optimizer is derived from its dual counterpart, whose derivation formsthe technical core of this article. A key challenge is that dual attainment isa subtle issue in martingale optimal transport, where dual optimizers may failto exist, even in highly regular settings.

Existence of Bass martingales and the martingale Benamou$-$Brenier problem in $\mathbb{R}^{d}$