Advanced Search
Article Contents
Article Contents

Stochastic deformation of classical mechanics

Abstract / Introduction Related Papers Cited by
  • We describe a method of stochastic deformation of classical mechanics preserving the time symmetry of this theory. It provides a new general strategy to deform stochastically Geometric Mechanics.
    Mathematics Subject Classification: Primary: 60H10, 49L99, 70F99.


    \begin{equation} \\ \end{equation}
  • [1]

    J. M. Bismut, "Mécanique Aléatoire", Springer-Verlag, Berlin, 1981.


    Xin Chen and A. B. CruzeiroStochastic geodesics and stochastic backward equations on Lie groups, in these proceedings.


    K. L. Chung and J.-C. Zambrini, "Introduction to Random Time and Quantum Randomness", World Scientific, 2003.


    A. B. Cruzeiro and J.-C. Zambrini, Malliavin calculus and Euclidean quantum mechanics. I. Functional calculus, J. Funct. Analysis, 96 (1991), 62-95.


    R. P. Feynman and A. R. Hibbs, "Quantum Mechanics and Path Integrals", McGraw-Hill, New York, 1965.


    W. H. Fleming and H. Mete Soner, "Controlled Markov Processes and Viscosity Solutions", $2^{nd}$ edition, Springer, 2006.


    N. Ikeda and S. Watanabe, "Stochastic Differential Equations and Diffusion Processes", North Holland, Amsterdam, 1981.


    J. A. Lázaro-Camí and J. P. Ortega, Stochastic Hamiltonian dynamical systems, Rep. Math. Phys., 61 (2008), 65-122.


    C. Leonard, From the Schrödinger problem to the Monge-Kantorovich problem, J. Funct. Anal., 262 (2012), 1879-1920.


    P. Lescot and J.-C. Zambrini, Probabilistic deformation of contact geometry, diffusion processes and their quadrature, Progress in Probability, Birkhäuser, 59 (2007), 203-226.


    N. Privault and J.-C. Zambrini, Markovian bridges and reversible diffusion processess with jumps, Ann. Inst. H. Poincaré, (Probability and Statistics) 40 (2004), 599-633.


    E. Schrödinger, Sur la theorie relativiste de l'électron et l'interprétation de la mécanique quantique, Ann. Inst. H. Poincaré, 2 (1932), 269-310.


    M. Thieullen and J.-C. Zambrini, Probability and quantum symmetries I. The theorem of Nœther in Schrödinger's Euclidean quantum mechanics}, Ann. Inst. H. Poincaré, (Phys. Théor.) 67 (1997), 297-338.


    G. E. Uhlenbeck and L. S. Ornstein, On the theory of the Brownian Motion, Physical Review, 36 (1930), 823-841.


    P. A. Vuillermot and J.-C. Zambrini, Bernstein Diffusions for a Class of Linear Parabolic Partial Differential Equations, Journal of Theoretical Probability, http://rd.springer.com/article/10.1007/s10959-012-0426-3, Springer-Verlag, 2012.


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


    J.-C. Zambrini, On the geometry of the Hamilton-Jacobi-Bellman equation, Journal of Geometric Mechanics, 1 (2009), 369-387.


    J.-C. ZambriniThe research program of stochastic deformation (with a view toward Geometric Mechanics), http://arxiv.org/abs/1212.4186

  • 加载中
Open Access Under a Creative Commons license

Article Metrics

HTML views() PDF downloads(121) Cited by(0)

Access History

Other Articles By Authors



    DownLoad:  Full-Size Img  PowerPoint