论文标题
存在用于局部对齐的随机羊群模型的Martingale解决方案
Existence of martingale solutions for stochastic flocking models with local alignment
论文作者
论文摘要
我们确定了一类随机保护方程的Martingale解决方案的存在。基础模型对应于用于集体运动的动力学模型的随机扰动，例如Cucker-Smale和Motsch-Tadmor模型。通过使系数正规化，我们首先构建作为相应粒子系统的平均场极限获得的近似溶液。然后，我们通过依靠随机平均引理来确定该解决方案家族的法律。这扩展了在确定性情况下由karper，mellet和Trivisa获得的结果。
We establish the existence of martingale solutions to a class of stochastic conservation equations. The underlying models correspond to random perturbations of kinetic models for collective motion such as the Cucker-Smale and Motsch-Tadmor models. By regularizing the coefficients, we first construct approximate solutions obtained as the mean-field limit of the corresponding particle systems. We then establish the compactness in law of this family of solutions by relying on a stochastic averaging lemma. This extends the results obtained by Karper, Mellet and Trivisa in the deterministic case.
