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Stochastic flows of an advective-diffusive nature are ubiquitous in physical sciences.
E. Schrödinger, “Über die Umkehrung der Naturgesetze,” Sitzungsberichte der Preuss Akad. Wissen. Phys. Math. Klasse, Sonderausgabe , vol. IX, pp. 144–153, 1931
1931
Earlier work this paper cites.
E. Schrödinger, “Sur la théorie relativiste de l’électron et l’interprétation de la mécanique quantique,” in Annales de l’institut Henri Poincaré , vol. 2, no. 4. Presses universitaires de France, 1932, pp. 269–310
1932
Earlier work this paper cites.
R. Fortet, “Résolution d’un systeme d’équations de M. Schrödinger,” J. Math. Pure Appl. IX , vol. 1, pp. 83–105, 1940
1940
Earlier work this paper cites.
G. Birkhoff, “Extensions of Jentzsch’s theorem,” Transactions of the American Mathematical Society , vol. 85, no. 1, pp. 219–227, 1957
1957
Earlier work this paper cites.
A. Beurling, “An automorphism of product measures,” Annals of Mathematics , pp. 189–200, 1960
1960
Earlier work this paper cites.
I. N. Sanov, “On the probability of large deviations of random variables,” Mat. Sb. N. S. / Selected Translations in Mathematical Statistics and Probability , vol. 42 / 1, pp. 11–44 / 213–244, 1957 / 1961
1961
Earlier work this paper cites.
S. S. Varadhan, “Asymptotic probabilities and differential equations,” Communications on Pure and Applied Mathematics , vol. 19, no. 3, pp. 261–286, 1966
1966
Earlier work this paper cites.
P. Bushell, “On the projective contraction ratio for positive linear mappings,” Journal of the London Mathematical Society , vol. 2, no. 2, pp. 256–258, 1973
1973
Earlier work this paper cites.
P. J. Bushell, “Hilbert’s metric and positive contraction mappings in a Banach space,” Archive for Rational Mechanics and Analysis , vol. 52, no. 4, pp. 330–338, 1973
1973
Earlier work this paper cites.
B. Jamison, “Reciprocal processes,” Z. Wahrscheinlichkeitstheorie verw. Gebiete , vol. 30, pp. 65–86, 1974
1974
Earlier work this paper cites.
B. Jamison, “The Markov processes of Schrödinger,” Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete , vol. 32, no. 4, pp. 323–331, 1975
1975
Earlier work this paper cites.
S. S. Varadhan, Large deviations and applications . SIAM, 1984
1984
Earlier work this paper cites.
J. Zambrini, “Stochastic mechanics according to E. Schrödinger,” Physical review A , vol. 33, no. 3, p. 1532, 1986
1986
Earlier work this paper cites.
H. Föllmer, “Random fields and diffusion processes,” in École d’Été de Probabilités de Saint-Flour XV–XVII, 1985–87 . Springer, 1988, pp. 101–203
1988
Earlier work this paper cites.
M. Nagasawa, “Transformations of diffusion and Schrödinger processes,” Probability theory and related fields , vol. 82, no. 1, pp. 109–136, 1989
1989
Earlier work this paper cites.
A. Wakolbinger, “A simplified variational characterization of Schrödinger processes,” Journal of mathematical physics , vol. 30, no. 12, pp. 2943–2946, 1989
1989
Earlier work this paper cites.
J. Franklin and J. Lorenz, “On the scaling of multidimensional matrices,” Linear Algebra and its applications , vol. 114, pp. 717–735, 1989
1989
Cited alongside, same era.
D. Dawson, L. Gorostiza, and A. Wakolbinger, “Schrödinger processes and large deviations,” Journal of mathematical physics , vol. 31, no. 10, pp. 2385–2388, 1990
1990
Cited alongside, same era.
M. Nagasawa, “Stochastic variational principle of Schrödinger processes,” in Seminar on Stochastic Processes, 1989 . Springer, 1990, pp. 165–175
1990
Cited alongside, same era.
A. Wakolbinger, “Schrödinger bridges from 1931 to 1991,” in Proc. of the 4th Latin American Congress in Probability and Mathematical Statistics, Mexico City , 1990, pp. 61–79
1990
Cited alongside, same era.
A. Blaquière, “Controllability of a Fokker-Planck equation, the Schrödinger system, and a related stochastic optimal control (revised version),” Dynamics and Control , vol. 2, no. 3, pp. 235–253, 1992
C. Léonard, “A survey of the Schrödinger problem and some of its connections with optimal transport,” Dicrete Contin. Dyn. Syst. A , vol. 34, no. 4, pp. 1533–1574, 2014
2014
Later among the works it cites.
Y. Chen, T. T. Georgiou, and M. Pavon, “Optimal steering of inertial particles diffusing anisotropically with losses,” in Proc. American Control Conf. , 2015, pp. 1252–1257
2015
Later among the works it cites.
T. T. Georgiou and M. Pavon, “Positive contraction mappings for classical and quantum Schrödinger systems,” Journal of Mathematical Physics , vol. 56, no. 3, p. 033301, 2015
2015
Later among the works it cites.
Y. Chen., T. Georgiou, and M. Pavon, “Optimal steering of a linear stochastic system to a final probability distribution, Part I,” IEEE Trans. on Automatic Control , vol. 61, no. 5, pp. 1158–1169, 2016
2016
Later among the works it cites.
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1992
Cited alongside, same era.
R. Aebi and M. Nagasawa, “Large deviations and the propagation of chaos for Schrödinger processes,” Probability Theory and Related Fields , vol. 94, no. 1, pp. 53–68, 1992
1992
Cited alongside, same era.
P. Billingsley, Convergence of probability measures . John Wiley & Sons, 1999
1999
Cited alongside, same era.
T. Mikami, “Monge’s problem with a quadratic cost by the zero-noise limit of h-path processes,” Probability theory and related fields , vol. 129, no. 2, pp. 245–260, 2004
2004
Cited alongside, same era.
T. Mikami and M. Thieullen, “Optimal transportation problem by stochastic optimal control,” SIAM Journal on Control and Optimization , vol. 47, no. 3, pp. 1127–1139, 2008
2008
Cited alongside, same era.
A. Dembo and O. Zeitouni, Large deviations techniques and applications . Springer Science & Business Media, 2009, vol. 38
2009
Cited alongside, same era.
S. N. Ethier and T. G. Kurtz, Markov processes: characterization and convergence . John Wiley & Sons, 2009, vol. 282
2009
Cited alongside, same era.
2011
Cited alongside, same era.
Y. Chen, T. T. Georgiou, and M. Pavon, “On the relation between optimal transport and Schrödinger bridges: A stochastic control viewpoint,” Journal of Optimization Theory and Applications , vol. 169, no. 2, pp. 671–691, 2016
2016
Later among the works it cites.
Y. Chen, T. Georgiou, and M. Pavon, “Entropic and displacement interpolation: a computational approach using the Hilbert metric,” SIAM Journal on Applied Mathematics , vol. 76, no. 6, pp. 2375–2396, 2016
2016
Later among the works it cites.
C. Léonard, “Lazy random walks and optimal transport on graphs,” The annals of Probability , vol. 44, no. 3, pp. 1864–1915, 2016
2016
Later among the works it cites.
2017
Later among the works it cites.
L. Chizat, G. Peyré, B. Schmitzer, and F.-X. Vialard, “Scaling algorithms for unbalanced optimal transport problems,” Mathematics of Computation , vol. 87, no. 314, pp. 2563–2609, 2018
2018
Later among the works it cites.
L. Chizat, G. Peyré, B. Schmitzer, and F.-X. Vialard, “Unbalanced optimal transport: Dynamic and Kantorovich formulations,” Journal of Functional Analysis , vol. 274, no. 11, pp. 3090–3123, 2018
2018
Later among the works it cites.
G. Conforti, “A second order equation for schrödinger bridges with applications to the hot gas experiment and entropic transportation cost,” Probability Theory and Related Fields , vol. 174, no. 1, pp. 1–47, 2019
2019
Later among the works it cites.
Y. Chen, T. T. Georgiou, and A. Tannenbaum, “Interpolation of matrices and matrix-valued densities: The unbalanced case,” European Journal of Applied Mathematics , vol. 30, no. 3, pp. 458–480, 2019
2019
Later among the works it cites.
Y. Chen, T. T. Georgiou, and M. Pavon, “Stochastic control liaisons: Richard Sinkhorn Meets Gaspard Monge on a Schrödinger bridge,” SIAM Review , vol. 63, no. 2, pp. 249–313, 2021
2021
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P. Koehl, M. Delarue, and H. Orland, “Physics approach to the variable-mass optimal-transport problem,” Physical Review E , vol. 103, no. 1, p. 012113, 2021
2021
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Y. Chen, T. T. Georgiou, and M. Pavon, “Optimal transport in systems and control,” Annual Review of Control, Robotics, and Autonomous Systems , vol. 4, pp. 89–113, 2021
2021
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