STOCHASTIC EULER-POINCARE REDUCTION

Abstract : 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.
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https://hal.archives-ouvertes.fr/hal-01057527
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Submitted on : Tuesday, September 9, 2014 - 4:36:00 PM
Last modification on : Wednesday, November 21, 2018 - 5:52:06 PM
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Marc Arnaudon, Xin Chen, Ana Bela Cruzeiro. STOCHASTIC EULER-POINCARE REDUCTION. 2014. ⟨hal-01057527⟩

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