15 citations · 24 across the 10 of their papers we have counts for
11 papers
Stochastic Geometric Mechanics in Nonequilibrium Thermodynamics: Schrödinger meets Onsager
Qiao Huang, Jean-Claude Zambrini
We are describing relations between Schrödinger's variational problem and Onsager's approach to nonequilibrium statistical mechanics. Although the second work on reciprocal relatio…
From Second-Order Differential Geometry to Stochastic Geometric Mechanics
Qiao Huang, Jean-Claude Zambrini
Classical geometric mechanics, including the study of symmetries, Lagrangian and Hamiltonian mechanics, and the Hamilton-Jacobi theory, are founded on geometric structures such as…
Stochastic geodesics
Ana Bela Cruzeiro, Jean-Claude Zambrini
We describe, in an intrinsic way and using the global chart provided by Ito's parallel transport, a generalisation of the notion of geodesic (as critical path of an energy function…
Time-symmetric optimal stochastic control problems in space-time domains
Ana Bela Cruzeiro, Carlos Oliveira, Jean-Claude Zambrini
We present a pair of adjoint optimal control problems characterizing a class of time-symmetric stochastic processes defined on random time intervals. The associated PDEs are of fre…
On Bernstein processes generated by hierarchies of linear parabolic systems in Rd
Pierre-A. Vuillermot, Jean-C. Zambrini
In this article we investigate the properties of Bernstein processes generated by infinite hierarchies of forward-backward systems of decoupled linear deterministic parabolic parti…
An entropic interpolation problem for incompressible viscid fluids
Marc Arnaudon, Ana Bela Cruzeiro, Christian Léonard +1
In view of studying incompressible inviscid fluids, Brenier introduced in the late 80's a relaxation of a geodesic problem addressed by Arnold in 1966. Instead of inviscid fluids,…
On some Gaussian Bernstein processes in RN and the periodic Ornstein-Uhlenbeck process
Pierre-A. Vuillermot, Jean-C. Zambrini
In this article we prove new results regarding the existence of Bernstein processes associated with the Cauchy problem of certain forward-backward systems of decoupled linear deter…
Solving stochastic differential equations with Cartan's exterior differential systems
Paul Lescot, Hélène Quintard, Jean-Claude Zambrini
The aim of this work is to use systematically the symmetries of the (one dimensional) bacward heat equation with potentiel in order to solve certain one dimensional Itô's stochasti…
Feynman-Kac formula for Levy processes and semiclassical (Euclidean) momentum representation
Nicolas Privault, Xiangfeng Yang, Jean-Claude Zambrini
We prove a version of the Feynman-Kac formula for Levy processes and integro-differential operators, with application to the momentum representation of suitable quantum (Euclidean)…
Reciprocal processes. A measure-theoretical point of view
Christian Léonard, Sylvie Roelly, Jean-Claude Zambrini
This is a survey paper about reciprocal processes. The bridges of a Markov process are also Markov. But an arbitrary mixture of these bridges fails to be Markov in general. However…
The research program of Stochastic Deformation (with a view toward Geometric Mechanics)
Jean-Claude Zambrini
We give an overview of a program of Stochastic Deformation of Classical Mechanics and the Calculus of Variations, strongly inspired by the quantization method.