Stochastic inviscid shell models: well-posedness and anomalous dissipation

In this paper we study a stochastic version of an inviscid shell model of turbulence with multiplicative noise. The deterministic counterpart of this model is quite general and includes inviscid GOY and Sabra shell models of turbulence. We prove global weak existence and uniqueness of solutions for any finite energy initial condition. Moreover energy dissipation of the system is proved in spite of its formal energy conservation.