4 papers · 1 filter
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…
Symmetries and martingales in a stochastic model for the Navier-Stokes equation
Ana Bela Cruzeiro, Rémi Lassalle
A stochastic description of solutions of the Navier-Stokes equation is investigated. These solutions are represented by laws of finite dimensional semi-martingales and characterize…
Backward Stochastic Differential Equations Associated with the Vorticity Equations
Ana Bela Cruzeiro, Zhongmin M. Qian
We derive a non-linear version of the Feynman-Kac formula for the solutions of the vorticity equation in dimension 2 with space periodic boundary conditions. We prove the existence…