A DIRICHLET PROCESS CHARACTERIZATION OF A CLASS OF REFLECTED DIFFUSIONS

• 成果类型: Article
• 署名作者: Kang, Weining; Ramanan, Kavita
• 署名单位: Carnegie Mellon University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/09-AOP487
• 发表日期: 2010
• 页码: 1062-1105
• 关键词: skorokhod problem; convex duality; DECOMPOSITION; FORMULA

摘要

For a class of stochastic differential equations with reflection for which a certain LP continuity condition holds with p > 1, it is shown that any weak solution that is a strong Markov process can be decomposed into the sum of a local martingale and a continuous, adapted process of zero p-variation. When p = 2, this implies that the reflected diffusion is a Dirichlet process. Two examples are provided to motivate such a characterization. The first example is a class of multidimensional reflected diffusions in polyhedral conical domains that arise as approximations of certain stochastic networks, and the second example is a family of two-dimensional reflected diffusions in curved domains. In both cases, the reflected diffusions are shown to be Dirichlet processes, but not semimartingales.