References

Here is a short and non exhaustive bibliography:

  1. Benamou, J. D., & Brenier, Y. (2000). A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem. Numerische Mathematik, 84(3), 375-393

  2. Benamou, J. D., Carlier, G., Cuturi, M., Nenna, L., & Peyré, G. (2015). Iterative Bregman projections for regularized transportation problems. SIAM Journal on Scientific Computing, 37(2), A1111-A1138,

  3. Beurling, A. (1960). An automorphism of product measures. Annals of Mathematics, 189-200

  4. Cruzeiro, A. B., Wu, L., & Zambrini, J. C. (2000). Bernstein processes associated with a Markov process. In Stochastic Analysis and Mathematical Physics (pp. 41-72). Birkhäuser, Boston, MA

  5. Galichon, A. (2016). Optimal transport methods in economics. Princeton University Press.


  1. Jamison, B. (1974). Reciprocal processes. Probability Theory and Related Fields, 30(1), 65-86

  2. Jammer, M. (1974). Philosophy of Quantum Mechanics. the interpretations of quantum mechanics in historical perspective, Wiley

  3. Lassalle, R., & Zambrini, J. C. (2016). A weak approach to the stochastic deformation of classical mechanics, Journal of Geometric Mechanics, 8(2)

  4. Léonard, C (2014). A survey of the Schrödinger problem and some of its connections with optimal transport. Discrete & Continuous Dynamical Systems - A, 34(4), 1533-1574

  5. Léonard, C., Rœlly, S., & Zambrini, J. C. (2014). Reciprocal processes. A measure-theoretical point of view. Probability Surveys, 11, 237-269,

  6. Villani, C. (2008). Optimal transport: old and new (Vol. 338). Springer Science & Business Media.

  7. Léonard, C. (2016). Lazy random walks and optimal transport on graphs. The Annals of Probability, 44(3), 1864-1915

  8. Vuillermot, P. A., & Zambrini, J. C. (2016). On some Gaussian Bernstein processes in and the periodic Ornstein–Uhlenbeck process. Stochastic Analysis and Applications, 34(4), 573-597

  9. Zambrini, J. C. (1986). Variational processes and stochastic versions of mechanics. Journal of Mathematical Physics, 27(9), 2307-2330

  10. Zambrini, J. C. (2015). The research program of Stochastic Deformation (with a view toward Geometric Mechanics). In Stochastic analysis: a series of lectures (pp. 359-393). Birkhäuser, Base