26 citations · 59 across the 24 of their papers we have counts for
29 papers
Stochastic perturbation of geodesics on the manifold of Riemannian metrics
Ana Bela Cruzeiro, Ali Suri
In this paper, using diffusion processes, we compute the evolution equation on the manifold of Riemannian metrics for the Lagrangian induced by the stochastic kinetic energy…
New invariant surface measures for the cubic Schrödinger equation
Jean-Baptiste Casteras, Ana Bela Cruzeiro, Annie Millet
We construct new invariant measures supported on mass level sets for the cubic defocusing nonlinear Schrödinger equation in dimensions and .
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…
On the well-posedness of a Hamilton-Jacobi-Bellman equation with transport noise
Neeraj Bhauryal, Ana Bela Cruzeiro, Carlos Oliveira
In this paper we consider the following non-linear stochastic partial differential equation (SPDE): \begin{align*} \begin{cases} \mathrm{d}u(s,x)=\sum^n_{i=1} \mathscr{L}_i u(s,x)\…
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…
Navier-Stokes and stochastic Navier-Stokes equations via Lagrange multipliers
Ana Bela Cruzeiro
We show that the Navier-Stokes as well as a random perturbation of this equation can be derived from a stochastic variational principle where the pressure is introduced as a Lagran…
On a non-periodic modified Euler equation: existence and quasi-invariant measures
Ana Bela Cruzeiro, Alexandra Symeonides
We consider a modified Euler equation on . We prove existence of weak global solutions for bounded (and fast decreasing at infinity) initial conditions and construct G…
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,…
Invariant measures for the non-periodic two-dimensional Euler equation
Ana Bela Cruzeiro, Alexandra Symeonides
We construct Gaussian invariant measures for the two-dimensional Euler equation on the plane. We show the existence of solution with initial conditions in the support of the measur…
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…
Momentum Maps and Stochastic Clebsch Action Principles
A. B. Cruzeiro, D. D. Holm, T. S. Ratiu
We derive stochastic differential equations whose solutions follow the flow of a stochastic nonlinear Lie algebra operation on a configuration manifold. For this purpose, we develo…
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…
Stochastic variational principles for dissipative equations with advected quantities
Xin Chen, Ana Bela Cruzeiro, Tudor S. Ratiu
This paper presents symmetry reduction for material stochastic Lagrangian systems with advected quantities whose configuration space is a Lie group. Such variational principles yie…
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…
Navier-Stokes equation and forward-backward stochastic differential system in the Besov spaces
Xin Chen, Ana Bela Cruzeiro, Zhongmin Qian
The Navier-Stokes equation on Rd (d greater or equal to 3) formulated on Besov spaces is considered. Using a stochastic forward-backward differential system, the local existence of…
Forward-backward systems of stochastic differential equations generated by Bernstein diffusions
Ana Bela Cruzeiro, Pierre-A. Vuillermot
In this short article we present new results that bring about hitherto unknown relations between certain Bernstein diffusions wandering in bounded convex domains of Euclidean space…
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…