Stochastic Euler-Poincaré reduction

Marc Arnaudon (1) , Xin Chen (2) , Ana Bela Cruzeiro (2)

1 IMB - Institut de Mathématiques de Bordeaux
2 grupo de fisica matematica

We prove a Euler-Poincaré reduction theorem for stochastic processes taking values on a Lie group, which is a generalization of the reduction argument in Marsden-Ratiu (2003) for the deterministic case. We also show examples of its application to SO(3) and to the group of diffeomorphisms, which includes the Navier-Stokes equation on a bounded domain and the Camassa-Holm equation.

Domaines: Probabilités [math.PR]

Marc Arnaudon, Xin Chen, Ana Bela Cruzeiro. Stochastic Euler-Poincaré reduction. Journal of Mathematical Physics, 2014, 55 (8), ⟨10.1063/1.4893357⟩. ⟨hal-01057527⟩