CLARK-OCONE FORMULA AND VARIATIONAL REPRESENTATION FOR POISSON FUNCTIONALS

• 成果类型: Article
• 署名作者: Zhang, Xicheng
• 署名单位: University of New South Wales Sydney; Huazhong University of Science & Technology
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/08-AOP411
• 发表日期: 2009
• 页码: 506-529
• 关键词: wentzell large deviations; brownian-motion; Levy processes

摘要

In this paper we first prove a Clark-Ocone formula for any bounded measurable functional on Poisson space. Then using this formula, under some conditions on the intensity measure of Poisson random measure, we prove a variational representation formula for the Laplace transform of bounded Poisson functionals, which has been conjectured by Dupuis and Ellis [A Weak Convergence Approach to the Theory of Large Deviations (1997) Wiley], p. 122.