On the Diameter of the Stopped Spider Process

• 成果类型: Article
• 署名作者: Bednarz, Ewelina; Ernst, Philip A.; OseRkowskia, Adam
• 署名单位: University of Warsaw; Imperial College London
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2023.1359
• 发表日期: 2024
• 关键词: martingale inequalities

摘要

We consider the Brownian spider process, also known as Walsh Brownian motion, first introduced by J. B. Walsh [Walsh JB (1978) A diffusion with a discontinuous local time. Asterisque 52:37-45]. The paper provides the best constant Cn for the inequality root ffiffiffiffififfi ED tau <= Cn E tau ,where tau is the class of all adapted and integrable stopping times and D denotes the diameter of the spider process measured in terms of the British rail metric. This solves a variant of the long-standing open spider problem due to L. E. Dubins. The proof relies on the explicit identification of the value function for the associated optimal stopping problem.