自稳定扩散过程间的Freidlin-Wentzell碰撞定律
Freidlin-Wentzell collision-laws between self-stabilizing diffusions
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中文总结 AI 辅助
该研究针对双稳态势中独立自稳定扩散过程，适配Freidlin-Wentzell估计推导其零噪声极限下的近碰撞渐近行为，还拓展至平均场粒子系统近似及一维情形。
中文摘要 AI 辅助
本研究考察一对独立的d维布朗驱动自稳定（McKean-Vlasov型）扩散过程在零噪声极限下首次近碰撞时间与首次近碰撞位置的渐近行为。研究考虑系统在双稳态势中演化、碰撞仅由布朗噪声共同作用触发的特殊情形。当布朗扰动消失时，近碰撞时间以显式指数速率增长，相关碰撞位置持续存在于空间特定区域。这些结果主要通过将经典Freidlin-Wentzell的首出时间（及首出位置）估计适配为碰撞估计得到，还为相关平均场相互作用粒子系统近似及一维情形（可检验真实碰撞）建立了类似渐近结果。
英文摘要
The present work investigates the asymptotic behaviours at the zero-noise limit of the first near collision-time and first near collision-location between a pair of independent $d$-dimensional Brownian-driven self-stabilizing (McKean-Vlasov type) diffusions. These asymptotic are considered in a peculiar setting where the systems evolve in a bi-stable landscape and collisions are only triggered by the combined action of the Brownian noises. As the Brownian perturbations fade away, we show that the near collision-time increases at an explicit exponential rate and that related collision-locations persist in specific regions of the space. These results are mainly derived by tailoring classical Freidlin-Wentzell's exit-time (and exit-location) estimates into collision estimates. Similar asymptotic are established for related mean-field interacting particle system approximation, and for the one-dimensional case (where true collisions can be examined
发表机构
- HSE University（高等经济大学）
- Université Jean Monnet（让·莫内大学）
机构由 AI 辅助整理，请以论文原文为准。
