无穷小漂移扰动Walsh蜘蛛过程
Perturbing Walsh's spider process by infinitesimal drifts
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中文总结 AI 辅助
本文研究星形图上Walsh过程受半渗透软膜扰动的极限行为，发现极限过程仍为Walsh型但参数需修改，与相关论文构成配套研究。
中文摘要 AI 辅助
我们考虑星形图上的Walsh过程，该过程受到以下事实的扰动：其路径需要额外穿过半渗透软膜，每个膜位于距中心小距离的不同边上，且每个膜具有各自的渗透系数。我们描述了当距离收敛到$0$时的极限过程，用逼近过程的特征来描述。主要发现是极限过程仍然是Walsh类型的，但其参数需要适当修改。本文是A. Bobrowski和A. Pilipenko的“On Portenko's approximation of skew Brownian motion”（arXiv:2601.20440）以及A. Pilipenko和G. Vilmart的“Limit theorems for one-dimensional diffusions: reflected, skew, sticky, skew-sticky, and snapping-out limits.”的密切配套论文。
英文摘要
We consider Walsh's process on a star graph perturbed by the fact that its paths need to additionally pass through semi-permeable soft membranes, each located on a different edge at a small distance from the center, and each having its own permeability coefficient. We describe the limit processes as the distances converge to $0$, in terms of the characteristics of the approximating ones. The main finding is that the limit process is still of Walsh type, but its parameters need to be appropriately modified. The paper is a close companion to A. Bobrowski and A. Pilipenko ``On Portenko's approximation of skew Brownian motion'' (arXiv:2601.20440), and to A. Pilipenko and G. Vilmart, ``Limit theorems for one-dimensional diffusions: reflected, skew, sticky, skew-sticky, and snapping-out limits.''
发表机构
- Lublin University of Technology（卢布林理工大学）
- University of Geneva, Section de mathématiques（日内瓦大学数学系）
- Institute of Mathematics of the Ukrainian National Academy of Sciences（乌克兰国家科学院数学研究所）
机构由 AI 辅助整理，请以论文原文为准。
