CHARACTERISTIC FUNCTIONS OF MEASURES ON GEOMETRIC ROUGH PATHS

• 成果类型: Article
• 署名作者: Chevyrev, Ilya; Lyons, Terry
• 署名单位: University of Oxford; University of Oxford
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/15-AOP1068
• 发表日期: 2016
• 页码: 4049-4082
• 关键词: signature; cubature; series

摘要

We define a characteristic function for probability measures on the signatures of geometric rough paths. We determine sufficient conditions under which a random variable is uniquely determined by its expected signature, thus partially solving the analogue of the moment problem. We furthermore study analyticity properties of the characteristic function and prove a method of moments for weak convergence of random variables. We apply our results to signature arising from Levy, Gaussian and Markovian rough paths.