Uniqueness for an inviscid stochastic dyadic model on a tree

In this paper we prove that the lack of uniqueness for solutions of the tree dyadic model of turbulence is overcome with the introduction of a suitable noise. The uniqueness is a weak probabilistic uniqueness for all $l^2$-initial conditions and is proven using a technique relying on the properties of the $q$-matrix associated to a continuous time Markov chain.

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