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Exploiting a fluid dynamic formulation for which a probabilistic counterpart might not be available, we extend the theory of Schroedinger bridges to the case of inertial particles with losses and general, possibly singular diffusion coefficient.
E. Schrödinger, Über die umkehrung der naturgesetze . Verlag Akademie der wissenschaften in kommission bei Walter de Gruyter u. Company, 1931
1931
Earlier work this paper cites.
——, “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.
A. Beurling, “An automorphism of product measures,” The Annals of Mathematics , vol. 72, no. 1, pp. 189–200, 1960
1960
Earlier work this paper cites.
L. Hörmander, “Hypoelliptic second order differential equations,” Acta Mathematica , vol. 119, no. 1, pp. 147–171, 1967
1967
Earlier work this paper cites.
O. A. Oleinik and E. V. Radkevich, “Second order equations with nonnegative characteristic form,” Itogi Nauki i Tekhniki. Seriya” Matematicheskii Analiz” , vol. 7, pp. 7–252, 1971
1971
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.
S. Karlin and H. M. Taylor, A second course in stochastic processes . Gulf Professional Publishing, 1981, vol. 2
1981
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.
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
Earlier work this paper cites.
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.
P. Dai Pra and M. Pavon, “On the Markov processes of Schrödinger, the Feynman-Kac formula and stochastic control,” in Realization and Modelling in System Theory . Springer, 1990, pp. 497–504
1990
Cited alongside, same era.
P. Perona and J. Malik, “Scale-space and edge detection using anisotropic diffusion,” Pattern Analysis and Machine Intelligence, IEEE Transactions on , vol. 12, no. 7, pp. 629–639, 1990
1990
Cited alongside, same era.
P. Dai Pra, “A stochastic control approach to reciprocal diffusion processes,” Applied mathematics and Optimization , vol. 23, no. 1, pp. 313–329, 1991
1991
Cited alongside, same era.
S. Feghhi, M. Shahriari, and H. Afarideh, “Calculation of neutron importance function in fissionable assemblies using Monte Carlo method,” Annals of Nuclear Energy , vol. 34, no. 6, pp. 514–520, 2007
2007
Later among the works it cites.
P. Guidotti, “Anisotropic diffusions of image processing from Perona-Malik on,” Advanced Studies in Pure Mathematics , vol. 99, p. 20XX, 2007
2007
Later among the works it cites.
A. Vinante, M. Bignotto, M. Bonaldi, M. Cerdonio, L. Conti, P. Falferi, N. Liguori, S. Longo, R. Mezzena, A. Ortolan et al. , “Feedback cooling of the normal modes of a massive electromechanical system to submillikelvin temperature,” Physical review letters , vol. 101, no. 3, p. 033601, 2008
2008
Later among the works it cites.
I. G. Vladimirov and I. R. Petersen, “Minimum relative entropy state transitions in linear stochastic systems: the continuous time case,” in Proceedings of 19th International Symposium on Mathematical Theory of Networks and Systems , 2010, pp. 51–58
2010
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1991
Cited alongside, same era.
I. Karatzas, Brownian motion and stochastic calculus . springer, 1991, vol. 113
1991
Cited alongside, same era.
J.-D. Benamou and Y. Brenier, “A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem,” Numerische Mathematik , vol. 84, no. 3, pp. 375–393, 2000
2000
Cited alongside, same era.
C. Villani, Topics in optimal transportation . American Mathematical Soc., 2003, no. 58
2003
Cited alongside, same era.
L. Ambrosio, N. Gigli, and G. Savaré, Gradient flows: in metric spaces and in the space of probability measures . Springer, 2006
2006
Cited alongside, same era.
——, “Optimal steering of a linear stochastic system to a final probability distribution, part II,” in preparation
Cited in the paper.
——, “Fast cooling for a system of stochastic oscillators,” in preparation
Cited in the paper.
Later among the works it cites.
T. Munakata and M. Rosinberg, “Feedback cooling, measurement errors, and entropy production,” Journal of Statistical Mechanics: Theory and Experiment , vol. 2013, no. 06, p. P06014, 2013
2013
Later among the works it cites.
2014
Closest in time.
M. Fischer, “On the form of the large deviation rate function for the empirical measures of weakly interacting systems,” Bernoulli , vol. 20, no. 4, pp. 1765–1801, 2014
2014
Closest in time.
U. Boscain, R. Chertovskih, J.-P. Gauthier, and A. Remizov, “Hypoelliptic diffusion and human vision: A semidiscrete new twist,” SIAM Journal on Imaging Sciences , vol. 7, no. 2, pp. 669–695, 2014
2014
Closest in time.