Characteristic functions of measures on geometric rough paths

• Ilya Chevyrev ^[1] ; Terry Lyons ^[1]
  1. [1] University of Oxford

     University of Oxford

     Oxford District, Reino Unido

     
• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 44, Nº. 6, 2016, págs. 4049-4082
• Idioma: inglés
• DOI: 10.1214/15-aop1068
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• Resumen

  • 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 Lévy, Gaussian and Markovian rough paths.