Symmetric cooperative motion in one dimension

• 成果类型: Article
• 署名作者: Addario-Berry, Louigi; Beckman, Erin; Lin, Jessica
• 署名单位: McGill University; Utah System of Higher Education; Utah State University
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-023-01244-2
• 发表日期: 2024
• 页码: 625-666
• 关键词: viscosity solutions; approximations; uniqueness

摘要

We explore the relationship between recursive distributional equations and convergence results for finite difference schemes of parabolic partial differential equations (PDEs). We focus on a family of random processes called symmetric cooperative motions, which generalize the symmetric simple random walk and the symmetric hipster random walk introduced in Addario-Berry et al. (Probab Theory Related fields 178(1-2):437-473, 2020). We obtain a distributional convergence result for symmetric cooperative motions and, along the way, obtain a novel proof of the Bernoulli central limit theorem. In addition, we prove a PDE result relating distributional solutions and viscosity solutions of the porous medium equation and the parabolic p-Laplace equation, respectively, in one dimension.