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Motivated by entropic optimal transport, time reversal of diffusion processes is revisited.
Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen
A. Einstein · 1905
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Über die Umkehrung der Naturgesetze
E. Schrödinger · 1931
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Sur la théorie relativiste de l’électron et l’interprétation de la mécanique quantique
E. Schrödinger · 1932
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Zur Theorie der Markoffschen Ketten
A. Kolmogorov · 1936
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Zur Umkehrbarkeit der statistischen Naturgesetze
A. Kolmogorov · 1937
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Markoff processes and potentials, III
G. A. Hunt · 1958
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The adjoint Markoff process
E. Nelson · 1958
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Time reversions of Markov processes
M. Nagasawa · 1964
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Quantum Mechanics and Path Integrals
R. Feynman and A. Hibbs · 1965
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On certain reversed processes and their applications to potential theory and boundary theory
H. Kunita and T. Watanabe · 1966
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Dynamical theories of Brownian motion
E. Nelson · 1967
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Absolute continuity of Markov processes and generators
H. Kunita · 1969
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Multidimensional diffusion processes
D.W. Stroock and S.R.S. Varadhan · 1979
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A non reversible semi-martingale
J. B. Walsh · 1982
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An application of flows to time shift and time reversal in stochastic processes
E. B. Dynkin · 1985
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An entropy approach to the time reversal of diffusion processes
H. Föllmer · 1985
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Time reversal on Wiener space
H. Föllmer · 1986
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Time reversal of diffusions
U. G. Haussmann and É. Pardoux · 1986
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Grossissement d’une filtration et retournement du temps d’une diffusion
É. Pardoux · 1986
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Variational processes and stochastic versions of mechanics
J.-C. Zambrini · 1986
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Gradient flows in metric spaces and in the space of probability measures
L. Ambrosio, N. Gigli, and G. Savaré · 2008
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A trajectorial approach to the gradient flow properties of Langevin-Smoluchowski diffusions
I. Karatzas, W. Schachermayer, and B. Tschiderer · 2008
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Optimal Transport. Old and New
C. Villani · 2009
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An optimal transport view on Schrödinger’s equation
M. von Renesse · 2011
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Girsanov theory under a finite entropy condition
C. Léonard · 2012
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Some properties of path measures
C. Léonard · 2014
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Large deviations from the McKean-Vlasov limit for weakly interacting diffusions
D.A. Dawson and J. Gärtner · 1987
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Probabilités et Potentiel. Ch. XII à XVI. Théorie du potentiel associée à une résolvante, théorie des processus de Markov
C. Dellacherie and P.-A. Meyer · 1987
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Random fields and diffusion processes, in École d’été de Probabilités de Saint-Flour XV-XVII-1985-87
H. Föllmer · 1988
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Large deviations, free energy functional and quasi-potential for a mean field model of interactiong diffusions
D. A. Dawson and J. Gärtner · 1989
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Integration by parts and time reversal for diffusion processes
A. Millet, D. Nualart, and M. Sanz · 1989
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Singular diffusions, time reversal and applications to Fokker-Planck equations
P. Cattiaux and F. Petit · 2001
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On the relation between optimal transport and Schrödinger bridges: A stochastic control viewpoint
Y. Chen, T. Georgiou, and M. Pavon · 2016
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A trajectorial interpretation of the dissipations of entropy and Fisher information for stochastic differential equations
J. Fontbona and B. Jourdain · 2016
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About the analogy between optimal transport and minimal entropy
I. Gentil, C. Léonard, and L. Ripani · 2017
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On the convexity of the entropy along entropic interpolations
C. Léonard · 2017
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A second order equation for Schrödinger bridges with applications to the hot gas experiment and entropic transportation cost
G. Conforti · 2019
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The mean field Schrödinger problem: ergodic behavior, entropy estimates and functional inequalities
J. Backhoff, G. Conforti, I. Gentil, and C. Léonard · 2020
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An entropic interpolation proof of the HWI inequality
I. Gentil, C. Léonard, L. Ripani, and L. Tamanini · 2020
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Time reversal of Markov processes with jumps under a finite entropy condition
G. Conforti and C. Léonard · 2022
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