LAUSR

This article studies the Stochastic Degasperis-Procesi equation on $$ \mathbb {R}$$ with an additive noise. Applying the kinetic theory, and considering the initial conditions in $$L^2(\mathbb {R})\cap L^{2+\delta }( \mathbb {R})$$ , for arbitrary small $$\delta >0$$ , we establish the existence of a global pathwise solution. Restricting to the particular case of zero noise, our result improves the deterministic solvability results that exist in the literature.