ON APPROXIMATE CONTINUITY AND THE SUPPORT OF REFLECTED STOCHASTIC DIFFERENTIAL EQUATIONS

• 成果类型: Article
• 署名作者: Ren, Jiagang; Wu, Jing
• 署名单位: Sun Yat Sen University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/15-AOP1018
• 发表日期: 2016
• 页码: 2064-2116
• 关键词: wong-zakai approximations; BOUNDARY; domain

摘要

In this paper we prove an approximate continuity result for stochastic differential equations with normal reflections in domains satisfying Saisho's conditions, which together with the Wong-Zakai approximation result completes the support theorem for such diffusions in the uniform convergence topology. Also by adapting Millet and Sanz-Sole's idea, we characterize in Holder norm the support of diffusions reflected in domains satisfying the Lions-Sznitman conditions by proving limit theorems of adapted interpolations. Finally we apply the support theorem to establish a boundary-interior maximum principle for subharmonic functions.