26 citations · 59 across the 24 of their papers we have counts for
4 papers · 1 filter
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…