两个相互作用的象随机游走的功能极限与首次分离时间
Functional Limits and Separation Times for Two Interacting Elephant Random Walks
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中文总结 AI 辅助
本文为相互作用双象模型建立功能极限，证明收敛到高斯过程，并研究首次分离时间的分布收敛与单调性。
中文摘要 AI 辅助
我们为Aguech和Qin研究的相互作用双象模型建立了功能尺度极限，并研究了首次分离时间。在联合扩散机制下，我们给出了收敛到二维连续高斯过程的直接鞅证明，该过程由噪声增强布朗运动的矩阵核类似物表示。随后我们研究了差分过程，其扩散尺度在对称情形下即使在联合游走处于临界或超扩散时仍然保持。对于两条游走的首次分离时间，我们建立了在分布上收敛到极限高斯过程的首出时间，以及在扩散尺度下所有正矩的收敛。通过结合显式协方差恒等式与Anderson不等式，我们还获得了极限首出时间的单调性结果。
英文摘要
We establish functional scaling limits and study first separation times for the interacting two elephant model studied by Aguech and Qin. In the joint diffusive regime, we give a direct martingale proof of convergence to a two-dimensional continuous Gaussian process represented by a matrix-kernel analogue of the noise-reinforced Brownian motion. We then investigate the difference process, whose diffusive scaling persists in the symmetric case even when the joint walk is critical or superdiffusive. For the first separation time of the two walks, we establish convergence in distribution to the first exit time of the limiting Gaussian process, together with convergence of all positive moments under diffusive scaling. We also obtain monotonicity results for the limiting exit time by combining explicit covariance identities with Anderson's inequality.
发表机构
- King Saud University（沙特国王大学）
- Kyushu University（九州大学）
机构由 AI 辅助整理，请以论文原文为准。
