26 citations · 59 across the 24 of their papers we have counts for
4 papers · 2 filters
Generalized Navier-Stokes flows and applications to incompressible viscous fluids
Alexandra Antoniouk, Marc Arnaudon, Ana Bela Cruzeiro
We introduce a notion of generalized stochastic flows on mani- folds, that extends to the viscous case the one defined by Brenier for perfect fluids. Their kinetic energy extends t…
Forward Backward Stochastic Differential Equations - Asymptotics and a Large Deviations Principle
Ana Bela Cruzeiro, André de Oliveira Gomes
We study the asymptotic behaviour of solutions of Forward Backward Stochastic Differential Equations in the coupled case, when the diffusion coefficient of the forward equation is…
Stochastic Euler-Poincaré reduction
Marc Arnaudon, Xin Chen, Ana Bela Cruzeiro
We prove a Euler-Poincaré reduction theorem for stochastic processes taking values in a Lie group and we show examples of its application to SO(3) and to the group of diffeomorphis…
Asymptotic Properties of Coupled Forward-Backward Stochastic Differential Equations
Ana Bela Cruzeiro, André de Oliveira Gomes, Liangquan Zhang
In this paper, we consider coupled forward-backward stochastic differential equations (FBSDEs in short) with parameter . We study the asymptotic behavior of its sol…