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Adapted or causal transport theory aims to extend classical optimal transport from probability measures to stochastic processes.
Decreasing sequences of measurable partitions and their applications
A. M. Vershik · 1970
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On the uniqueness of solutions of stochastic differential equations
T. Yamada and S. Watanabe · 1971
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Borel parametrizations
R. D. Mauldin · 1979
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Weak convergence and general theory of processes
D. J. Aldous · 1981
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Adapted probability distributions
D. N. Hoover and H. J. Keisler · 1984
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The Wasserstein distance and approximation theorems
L. Rüschendorf · 1985
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Convergence in distribution and Skorokhod convergence for the general theory of processes
D. Hoover · 1991
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Theory of decreasing sequences of measurable partitions
A. M. Vershik · 1994
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Classical descriptive set theory
A. S. Kechris · 1995
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Sequential decisions under uncertainty and the maximum theorem
M. F. Hellwig · 1996
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The Monge mass transfer problem and its applications
W. Gangbo · 1999
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Foundations of Modern Probability
O. Kallenberg · 2002
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Lecture notes on optimal transport problems
L. Ambrosio · 2003
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Topics in Optimal Transportation
C. Villani · 2003
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On the geometry of the space of probability measures in ℝ n \mathbb{R}^{n} endowed with the quadratic optimal transport distance
N. Gigli · 2004
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Infinite Dimensional Analysis - A Hitchhiker’s Guide
C. D. Aliprantis and K. C. Border · 2007
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The Yamada–Watanabe–Engelbert theorem for general stochastic equations and inequalities
T. Kurtz · 2007
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On the equality between Monge’s infimum and Kantorovich’s minimum in optimal mass transportation
A. Pratelli · 2007
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Optimal Transport, Old and New
C. Villani · 2009
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A distance for multistage stochastic optimization models
G. C. Pflug and A. Pichler · 2012
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Causal optimal transport and its links to enlargement of filtrations and continuous-time stochastic optimization
B. Acciaio, J. Backhoff-Veraguas, and A. Zalashko · 2020
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Adapted Wasserstein distances and stability in mathematical finance
J. Backhoff-Veraguas, D. Bartl, M. Beiglböck, and M. Eder · 2020
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All adapted topologies are equal
J. Backhoff-Veraguas, D. Bartl, M. Beiglböck, and M. Eder · 2020
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Continuity of utility maximization under weak convergence
E. Bayraktar, Y. Dolinsky, and J. Guo · 2020
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Extended weak convergence and utility maximisation with proportional transaction costs
E. Bayraktar, L. Dolinskyi, and Y. Dolinsky · 2020
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Causal transference plans and their Monge–Kantorovich problems
R. Lassalle · 2018
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New algorithms and fast implementations to approximate stochastic processes
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Weak transport for non-convex costs and model-independence in a fixed-income market
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Mathematical foundations of distributionally robust multistage optimization
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Adapted topologies and higher rank signatures
P. Bonnier, C. Liu, and H. Oberhauser · 2023
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The Wasserstein space of stochastic processes
D. Bartl, M. Beiglböck, and G. Pammer · 2024
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