26 citations · 59 across the 24 of their papers we have counts for
19 papers · 1 filter
Forward-backward stochastic differential equations on tensor fields and application to Navier-Stokes equations on Riemannian manifolds
Xin Chen, Ana Bela Cruzeiro, Wenjie Ye +1
In this paper we introduce a class of forward-backward stochastic differential equations on tensor fields of Riemannian manifolds, which are related to semi-linear parabolic partia…
Pathwise stochastic control and a class of stochastic partial differential equations
Neeraj Bhauryal, Ana Bela Cruzeiro, Carlos Oliveira
We consider a pathwise stochastic optimal control problem and study the associated (not necessarily adapted) Hamilton-Jacobi-Bellman stochastic partial differential equation. We sh…
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…
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,…
Barrier Option Pricing under the 2-Hypergeometric Stochastic Volatility Model
Rúben Sousa, Ana Bela Cruzeiro, Manuel Guerra
We investigate the pricing of financial options under the 2-hypergeometric stochastic volatility model. This is an analytically tractable model that reproduces the volatility smile…
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…
Generalized stochastic Lagrangian paths for the Navier-Stokes equation
Marc Arnaudon, Ana Bela Cruzeiro, Shizan Fang
In the note added in proof of the seminal paper [Groups of diffeomorphisms andthe motion of an incompressible fluid, Ann. of Math. 92 (1970), 102-163], Ebinand Marsden introduced t…
A stochastic variational approach to the viscous Camassa-Holm and Leray-alpha equations
Ana Bela Cruzeiro, Guoping Liu
We derive the (d-dimensional) periodic incompressible and viscous Camassa-Holm equation as well as the Leray-alpha equations via a stochastic variational principle. We discuss the…
Weak calculus of variations for functionals of laws of semi-martingales
Ana Bela Cruzeiro, Rémi Lassalle
We develop a non-anticipating calculus of variations for functionals on a space of laws of continuous semi-martingales, which extends the classical one. We extend Hamilton's least…
On a 2D stochastic Euler equation of transport type: existence and geometric formulation
Ana Bela Cruzeiro, Iván Torrecilla
We prove weak existence of Euler equation (or Navier-Stokes equation) perturbed by a multiplicative noise on bounded domains of with Dirichlet boundary conditions and…
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…
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…
Lagrangian Navier-Stokes diffusions on manifolds: variational principle and stability
Marc Arnaudon, Ana Bela Cruzeiro
We prove a variational principle for stochastic Lagrangian Navier-Stokes trajectories on manifolds. We study the behaviour of such trajectories concerning stability as well as rota…
On a forward-backward stochastic system associated to the Burgers equation
Ana Bela Cruzeiro, Evelina Shamarova
We describe a probabilistic construction of -regular solutions for the spatially periodic forced Burgers equation by using a characterization of this solution through a forwar…
Navier-Stokes equations and forward-backward SDEs on the group of diffeomorphisms of a torus
Ana Bela Cruzeiro, Evelina Shamarova
We establish a connection between the strong solution to the spatially periodic Navier-Stokes equations and a solution to a system of forward-backward stochastic differential equat…