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.

中文翻译：

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随机 Degasperis-Procesi 方程的可解性

本文研究了带有加性噪声的\( \mathbb {R}\)上的 Stochastic Degasperis-Procesi 方程。应用动力学理论，并考虑\(L^2(\mathbb {R})\cap L^{2+\delta }( \mathbb {R})\) 中的初始条件，对于任意小的\(\delta >0\)，我们建立了全局路径解的存在。限于零噪声的特殊情况，我们的结果改进了文献中存在的确定性可解性结果。