由Lévy噪声驱动的具有时滞的McKean-Vlasov p-Laplacian格点系统测度吸引子的存在性及消失噪声极限
Existence and vanishing noise limit of measure attractors for McKean-Vlasov $p$-Laplacian lattice systems with delay driven by Lévy noise
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中文总结 AI 辅助
研究由Lévy噪声驱动的带时滞的McKean-Vlasov随机p-Laplace格点系统，证明右连左极解存在唯一，定义非自治余圈，证明其相关性质及拉回测度吸引子的存在唯一性，还研究了噪声强度趋于零时测度吸引子的极限行为及收敛速率。
中文摘要 AI 辅助
本文关注由Lévy噪声驱动的具有时滞的McKean-Vlasov随机p-Laplace格点系统解段过程分布律的测度吸引子的存在性和极限行为。允许非线性漂移和扩散项有超线性增长。由于时滞，采用Skorohod度量空间描述带跳跃解的轨迹。首先证明格点系统右连左极解的存在唯一性，定义一个作用在Skorohod空间中Borel概率测度上的非自治余圈，证明其存在拉回吸收集、渐近紧性及拉回测度吸引子的存在唯一性。最后研究格点系统测度吸引子在噪声强度趋于零时的极限行为，建立单点子测度吸引子在θ阶Wasserstein距离下的最优收敛速率。
英文摘要
This paper is concerned with the existence and the limiting behavior of measure attractors of distribution laws of the solution segment process for the McKean-Vlasov stochastic $p$-Laplace lattice system with time delay driven by Lévy noise. The nonlinear drift and diffusion terms are allowed to have superlinear growth. Due to time delay, the Skorohod metric space is employed to describe the trajectories of the solutions with jumps. We first prove the existence and uniqueness of càdlàg solutions for the lattice system, and then define a non-autonomous cocycle acting on the Borel probability measures in the Skorohod space. This cocycle is continuous in bounded subsets of the space of probability measures only when time is sufficiently large. We then prove the existence of pullback absorbing sets and the asymptotic compactness of the cocycle as well as the existence and uniqueness of pullback measure attractors. We finally investigate the limiting behavior of measure attractors of the lattice system as the noise intensity approaches zero, and establish the optimal convergence rate of singleton measure attractors in the Wasserstein distance of order $θ$.
