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Stochastic deformation of classical mechanics
1. | Grupo de Física Matemática, Instituto para a Investigação Interdisciplinar da Universidade de Lisboa, Av. Prof. Gama Pinto, 2, PT-1649-003 Lisboa, Portugal |
References:
[1] |
J. M. Bismut, "Mécanique Aléatoire", Springer-Verlag, Berlin, 1981. |
[2] |
Xin Chen and A. B. Cruzeiro, Stochastic geodesics and stochastic backward equations on Lie groups,, in these proceedings., ().
|
[3] |
K. L. Chung and J.-C. Zambrini, "Introduction to Random Time and Quantum Randomness", World Scientific, 2003. |
[4] |
A. B. Cruzeiro and J.-C. Zambrini, Malliavin calculus and Euclidean quantum mechanics. I. Functional calculus, J. Funct. Analysis, 96 (1991), 62-95. |
[5] |
R. P. Feynman and A. R. Hibbs, "Quantum Mechanics and Path Integrals", McGraw-Hill, New York, 1965. |
[6] |
W. H. Fleming and H. Mete Soner, "Controlled Markov Processes and Viscosity Solutions", $2^{nd}$ edition, Springer, 2006. |
[7] |
N. Ikeda and S. Watanabe, "Stochastic Differential Equations and Diffusion Processes", North Holland, Amsterdam, 1981. |
[8] |
J. A. Lázaro-Camí and J. P. Ortega, Stochastic Hamiltonian dynamical systems, Rep. Math. Phys., 61 (2008), 65-122. |
[9] |
C. Leonard, From the Schrödinger problem to the Monge-Kantorovich problem, J. Funct. Anal., 262 (2012), 1879-1920. |
[10] |
P. Lescot and J.-C. Zambrini, Probabilistic deformation of contact geometry, diffusion processes and their quadrature, Progress in Probability, Birkhäuser, 59 (2007), 203-226. |
[11] |
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. |
[12] |
E. Schrödinger, Sur la theorie relativiste de l'électron et l'interprétation de la mécanique quantique, Ann. Inst. H. Poincaré, 2 (1932), 269-310. |
[13] |
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. |
[14] |
G. E. Uhlenbeck and L. S. Ornstein, On the theory of the Brownian Motion, Physical Review, 36 (1930), 823-841. |
[15] |
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. |
[16] |
J.-C. Zambrini, Variational processes and stochastic versions of mechanics, J. Math. Physics, 27(9) (1986), 2307-2330. |
[17] |
J.-C. Zambrini, On the geometry of the Hamilton-Jacobi-Bellman equation, Journal of Geometric Mechanics, 1 (2009), 369-387. |
[18] |
J.-C. Zambrini, The research program of stochastic deformation (with a view toward Geometric Mechanics),, , ().
|
show all references
References:
[1] |
J. M. Bismut, "Mécanique Aléatoire", Springer-Verlag, Berlin, 1981. |
[2] |
Xin Chen and A. B. Cruzeiro, Stochastic geodesics and stochastic backward equations on Lie groups,, in these proceedings., ().
|
[3] |
K. L. Chung and J.-C. Zambrini, "Introduction to Random Time and Quantum Randomness", World Scientific, 2003. |
[4] |
A. B. Cruzeiro and J.-C. Zambrini, Malliavin calculus and Euclidean quantum mechanics. I. Functional calculus, J. Funct. Analysis, 96 (1991), 62-95. |
[5] |
R. P. Feynman and A. R. Hibbs, "Quantum Mechanics and Path Integrals", McGraw-Hill, New York, 1965. |
[6] |
W. H. Fleming and H. Mete Soner, "Controlled Markov Processes and Viscosity Solutions", $2^{nd}$ edition, Springer, 2006. |
[7] |
N. Ikeda and S. Watanabe, "Stochastic Differential Equations and Diffusion Processes", North Holland, Amsterdam, 1981. |
[8] |
J. A. Lázaro-Camí and J. P. Ortega, Stochastic Hamiltonian dynamical systems, Rep. Math. Phys., 61 (2008), 65-122. |
[9] |
C. Leonard, From the Schrödinger problem to the Monge-Kantorovich problem, J. Funct. Anal., 262 (2012), 1879-1920. |
[10] |
P. Lescot and J.-C. Zambrini, Probabilistic deformation of contact geometry, diffusion processes and their quadrature, Progress in Probability, Birkhäuser, 59 (2007), 203-226. |
[11] |
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. |
[12] |
E. Schrödinger, Sur la theorie relativiste de l'électron et l'interprétation de la mécanique quantique, Ann. Inst. H. Poincaré, 2 (1932), 269-310. |
[13] |
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. |
[14] |
G. E. Uhlenbeck and L. S. Ornstein, On the theory of the Brownian Motion, Physical Review, 36 (1930), 823-841. |
[15] |
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. |
[16] |
J.-C. Zambrini, Variational processes and stochastic versions of mechanics, J. Math. Physics, 27(9) (1986), 2307-2330. |
[17] |
J.-C. Zambrini, On the geometry of the Hamilton-Jacobi-Bellman equation, Journal of Geometric Mechanics, 1 (2009), 369-387. |
[18] |
J.-C. Zambrini, The research program of stochastic deformation (with a view toward Geometric Mechanics),, , ().
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