Abstract In this work, we consider sub-critical and critical models for viscoelastic flows driven by pure jump Levy noise. Due to the elastic property, the noise in the equation for the stress tensor is considered in the Marcus canonical form. We investigate existence of a weak martingale solution for stochastic Oldroyd-B models, with full dissipation in whole of R d , d = 2 , 3 . The key ingredients of the proof are classical Faedo-Galerkin approximation, the compactness method and the Jakubowski version of the Skorokhod Theorem for nonmetric spaces. Pathwise uniqueness, existence of a strong solution and uniqueness in law for the two-dimensional model are also shown. We also prove, in a Poincare domain in two-dimensions, existence of an invariant measure using bw-Feller property of the associated Markov semigroup.

中文翻译：

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跳跃噪声驱动的随机Oldroyd-B型模型的弱解和不变测度

摘要 在这项工作中，我们考虑了由纯跳跃 Levy 噪声驱动的粘弹性流动的亚临界和临界模型。由于弹性属性，应力张量方程中的噪声在 Marcus 规范形式中被考虑。我们研究了随机 Oldroyd-B 模型的弱鞅解的存在，在整个 R d , d = 2 , 3 中完全耗散。证明的关键要素是经典的 Faedo-Galerkin 近似、紧致方法和非度量空间的 Skorokhod 定理的 Jakubowski 版本。还显示了二维模型的路径唯一性、强解的存在性和定律唯一性。我们还证明，在二维庞加莱域中，使用相关马尔可夫半群的 bw-Feller 性质，存在不变测度。