Abstract
In this paper, the stochastic Camassa–Holm equation with pure jump noise in the Marcus form is considered. Firstly, the equation is derived by the stochastic variation method. Then, wave-breaking is shown to occur in expectation. Furthermore, the global existence is obtained under suitable initial conditions. Finally, a moderate deviation principle is proved by the regularized equation, the weak convergence method and an exponential equivalence of the probability measures.
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