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We revisit the variational characterization of diffusion as entropic gradient flux and provide for it a probabilistic interpretation based on stochastic calculus.
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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
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M. Nagasawa · 1964
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A. Friedman · 1975
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Logarithmic Sobolev Inequalities
L. Gross · 1975
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An Application of Time Reversal of Markov Processes to a Problem of Population Genetics
M. Nagasawa and T. Maruyama · 1979
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Singular Perturbation Methods in Stochastic Differential Equations of Mathematical Physics
Z. Schuss · 1980
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A non reversible semi-martingale
J. B. Walsh · 1982
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E. A. Carlen · 1984
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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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Integration by Parts and Time Reversal for Diffusion Processes
A. Millet, D. Nualart, and M. Sanz · 1989
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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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Schrödinger Equations and Diffusion Theory
M. Nagasawa · 1993
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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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Degenerate Stochastic Differential Equations and Hypoellipticity
D. R. Bell · 1995
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R. Jordan and D. Kinderlehrer · 1996
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H. Risken · 1996
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Louis Bachelier’s Theory of Speculation: The Origins of Modern Finance — Translated and with Commentary by Mark Davis & Alison Etheridge
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T. M. Cover and J. A. Thomas · 2006
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The Malliavin Calculus and Related Topics
D. Nualart · 2006
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On the geometry of metric measure spaces I
K.-T. Sturm · 2006
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On the geometry of metric measure spaces II
K.-T. Sturm · 2006
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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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M. Talagrand · 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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Brownian Motion and Stochastic Calculus
I. Karatzas and S. E. Shreve · 1998
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A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem
J.-D. Benamou and Y. Brenier · 2000
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On the trend to equilibrium for the Fokker-Planck equation: an interplay between physics and functional analysis
P. A. Markowich and C. Villani · 2000
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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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A User’s Guide to Optimal Transport
L. Ambrosio and N. Gigli · 2013
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Analysis and Geometry of Markov Diffusion Operators
D. Bakry, I. Gentil, and M. Ledoux · 2014
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Logarithmic Sobolev inequality for diffusion semigroups
I. Gentil · 2014
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Some Properties of Path Measures
C. Léonard · 2014
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Pathwise versions of the Burkholder-Davis-Gundy inequality
M. Beiglböck and P. Siorpaes · 2015
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A gradient flow approach to large deviations for diffusion processes
M. Fathi · 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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On the convexity of the entropy along entropic interpolations
C. Léonard · 2017
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Pathwise Otto calculus and the likelihood ratio process as a backwards martingale
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Dynamical aspects of the generalized Schrödinger problem via Otto calculus — A heuristic point of view
I. Gentil, C. Léonard, and L. Ripani · 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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