Mathias Beiglbock

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math.PR2026

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

Julio Backhoff-Veraguas, Mathias BeiglbÃ¶ck, Walter Schachermayer +1

In classical optimal transport, the contributions of Benamou $-$ Brenier and McCann regarding the time-dependent version of the problem are cornerstones of the field and form the bas…

math.PR2026

Bridging classical and martingale SchrÃ¶dinger bridges

Julio Backhoff, Mathias BeiglbÃ¶ck, Giorgia Bifronte +1

We investigate the martingale SchrÃ¶dinger bridge, recently introduced by Nutz and Wiesel as a distinguished martingale transport plan between two probability measures in convex or…

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

Strassen's theorem for biased convex order

Beatrice Acciaio, Mathias BeiglbÃ¶ck, Evgeny Kolosov +1

Strassen's theorem asserts that for given marginal probabilities $I^¼, I^½$ there exists a martingale starting in $I^¼$ and terminating in $I^½$ if and only if $I^¼, I^½$ are in convex ord…

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…

Existence of Bass martingales and the martingale Benamou−Brenier problem in Rd

Bridging classical and martingale SchrÃ¶dinger bridges

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

Denseness of biadapted Monge mappings

Strassen's theorem for biased convex order

The Fundamental Theorem of Weak Optimal Transport

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

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