A geometrical characterization of multidimensional Hausdorff polytopes with applications to exit time problems

• 成果类型: Article
• 署名作者: Helmes, Kurt; Roehl, Stefan
• 署名单位: Humboldt University of Berlin
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.1070.0293
• 发表日期: 2008
• 页码: 315-326
• 关键词: markov-processes; optimality; moments

摘要

We present a formula for the corner points of the multidimensional Hausdorff polytopes and show how this result can be used to improve linear programming models for computing, e.g., moments of exit time distributions of diffusion processes. Specifically, we compute the mean exit time of two-dimensional Brownian motion from the unit square, as well as higher moments of the exit time of time-space Brownian motion, i.e., the two-dimensional process composed of a one-dimensional Wiener process and the time component, from a rectangle. The corner point formula is complemented by a convergence result, which provides the analytical underpinning of the numerical method that we use.