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In this work we study a stochastic three-dimensional Landau–Lifshitz–Gilbert equation perturbed by pure jump noise in the Marcus canonical form. We show the existence of a weak martingale solution taking values in a two-dimensional sphere $${\mathbb{S}^2}$$ and discuss certain regularity results. The construction of a solution is based on the classical Faedo–Galerkin approximation, the compactness methods and the Jakubowski version of the Skorokhod Theorem for nonmetric spaces.

In this work we prove the existence and uniqueness of the strong solution of the shell model of turbulence perturbed by Levy noise. The local monotonicity arguments have been exploited in the proofs.