Applications of Strassen's theorem and Choquet theory to optimal transport problems, to uniformly convex functions and to uniformly smooth functions

DOI10.1016/j.na.2023.113267zbMath1525.46004arXiv2001.11292OpenAlexW4323536744WikidataQ122733981 ScholiaQ122733981MaRDI QIDQ6097522

Krzysztof J. Ciosmak

Publication date: 5 June 2023

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2001.11292

zbMATH Keywords

uniform convexityoptimal transportKantorovich dualityStrassen's disintegration theorem

Mathematics Subject Classification ID

Martingales with discrete parameter (60G42) Optimality conditions and duality in mathematical programming (90C46) Monotone operators and generalizations (47H05) Duality theory (optimization) (49N15) Applications of functional analysis in probability theory and statistics (46N30) Convexity of real functions of several variables, generalizations (26B25) Convex sets in topological linear spaces; Choquet theory (46A55) Linear optimal control problems (49N05)

Cites Work

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• On a problem of optimal transport under marginal martingale constraints
• Duality theorem for the stochastic optimal control problem
• The disintegration of the Lebesgue measure on the faces of a convex function
• The Skorokhod embedding problem and its offspring
• Hadamard and Tyhonov well-posedness of a certain class of convex functions
• An abstract disintegration theorem
• Invariance principles in probability for triangular arrays of B-valued random vectors and some applications
• Convexity, monotonicity, and gradient processes in Hilbert space
• On the Strassen disintegration theorem
• Structure of optimal martingale transport plans in general dimensions
• A general duality theorem for marginal problems
• Uniformly convex and uniformly smooth convex functions
• Analyse convexe et ses applications. Comptes rendus, janvier 1974
• Strassen disintegration theorems
• Leaves decompositions in Euclidean spaces
• Optimal transport of vector measures
• Sharp and rigid isoperimetric inequalities in metric-measure spaces with lower Ricci curvature bounds
• Optimal transport and Skorokhod embedding
• Dual attainment for the martingale transport problem
• A stochastic control approach to no-arbitrage bounds given marginals, with an application to lookback options
• A simple proof of duality theorem for Monge-Kantorovich problem
• Fréchet differentiability of convex functions
• On mass transportation
• On a problem of Monge
• A general duality theorem for the Monge–Kantorovich transport problem
• Duality for Borel measurable cost functions
• Uniqueness and Monge Solutions in the Multimarginal Optimal Transportation Problem
• Every Convex Function is Locally Lipschitz
• Duality theorems for marginal problems
• Multi-marginal optimal transport: Theory and applications
• Optimal transportation for the determinant
• Extreme Points of Moment Sets
• Monotone Operators and the Proximal Point Algorithm
• Optimal maps for the multidimensional Monge-Kantorovich problem
• Duality and perfect probability spaces
• Book Review: Geometry of isotropic convex bodies
• A General Condition for Monge Solutions in the Multi-Marginal Optimal Transport Problem
• The Existence of Probability Measures with Given Marginals
• Gradients of Convex Functions
• Optimal Transport
• On uniformly convex functions

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