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We revisit the variational characterization of conservative diffusion as entropic gradient flow and provide for it a probabilistic interpretation based on stochastic calculus.
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A. N. Kolmogorov · 1931
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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 Umkehrbarkeit der statistischen Naturgesetze
A. N. Kolmogorov · 1937
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Some Inequalities Satisfied by the Quantities of Information of Fisher and Shannon
A. J. Stam · 1959
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Diffusions hypercontractives
D. Bakry and M. Émery · 1985
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An entropy approach to the time reversal of diffusion processes
H. Föllmer · 1985
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Smooth Transition Densities for One-Dimensional Diffusion
L. C. G. Rogers · 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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Brownian Motion and Stochastic Calculus
I. Karatzas and S. E. Shreve · 1988
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Polar Factorization and Monotone Rearrangement of Vector-Valued Functions
Y. Brenier · 1991
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Entropy Production by Block Variable Summation and Central Limit Theorems
E. A. Carlen and A. Soffer · 1991
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D. Williams · 1991
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A Deterministic Approach to Optimal Stopping
M. H. A. Davis and I. Karatzas · 1994
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Sur une transformation du mouvement brownien due à Jeulin et Yor
P. A. Meyer · 1994
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An extended variational principle
R. Jordan and D. Kinderlehrer · 1996
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The Fokker-Planck Equation — Methods of Solution and Applications
H. Risken · 1996
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A Convexity Principle for Interacting Gases
R. J. McCann · 1997
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The Variational Formulation of the Fokker-Planck Equation
R. Jordan, D. Kinderlehrer, and F. Otto · 1998
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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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Stochastic Methods — A Handbook for the Natural and Social Sciences
C. Gardiner · 2009
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Optimal Transport — Old and New
C. Villani · 2009
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Transport Inequalities. A Survey
N. Gozlan and C. Léonard · 2010
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A trajectorial interpretation of Doob’s martingale inequalities
B. Acciaio, M. Beiglböck, F. Penkner, W. Schachermayer, and J. Temme · 2013
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Large deviations and gradient flows
S. Adams, N. Dirr, M. Peletier, and J. Zimmer · 2013
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