Stefan Schrott

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math.PR2025

A Brenier Theorem on $(P_{2} (... P_{2} (H) ...), W_{2})$ and Applications to Adapted Transport

Mathias BeiglbÃ¶ck, Gudmund Pammer, Stefan Schrott

We develop Brenier theorems on iterated Wasserstein spaces. For a separable Hilbert space $H$ and $N \geq 1$ , we construct a full-support probability $I^$ on $P_2^{N}(H)= P_2(... P_…

math.PR2025

Denseness of biadapted Monge mappings

Mathias BeiglbÃ¶ck, Gudmund Pammer, Stefan Schrott

Adapted or causal transport theory aims to extend classical optimal transport from probability measures to stochastic processes. On a technical level, the novelty is to restrict to…

math.PR2025

On Strassen's Theorem for support functions

Stefan Schrott, Daniel Toneian

Strassen established that there exists a two step martingale with marginal distributions $I^¼$ , $I^½$ if and only if $I^¼$ , $I^½$ are in convex order. Recently ChonÃ©-Gozlan-Kramarz ob…

math.PR2025

The Fundamental Theorem of Weak Optimal Transport

Mathias BeiglbÃ¶ck, Gudmund Pammer, Lorenz Riess +1

The fundamental theorem of classical optimal transport establishes strong duality and characterizes optimizers through a complementary slackness condition. Milestones such as Breni…

math.PR2025

The Wasserstein Space of Stochastic Processes in Continuous Time

Daniel Bartl, Mathias BeiglbÃ¶ck, Gudmund Pammer +2

Researchers from different areas have independently defined extensions of the usual weak convergence of laws of stochastic processes with the goal of adequately accounting for the…

A Brenier Theorem on (P2​(...P2​(H)...),W2​) and Applications to Adapted Transport

Denseness of biadapted Monge mappings

On Strassen's Theorem for support functions

The Fundamental Theorem of Weak Optimal Transport

The Wasserstein Space of Stochastic Processes in Continuous Time

A Brenier Theorem on $(P_{2} (... P_{2} (H) ...), W_{2})$ and Applications to Adapted Transport