WEAK SYMMETRIC INTEGRALS WITH RESPECT TO THE FRACTIONAL BROWNIAN MOTION

• 成果类型: Article
• 署名作者: Binotto, Giulia; Nourdin, Ivan; Nualart, David
• 署名单位: University of Barcelona; University of Luxembourg; University of Kansas
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/17-AOP1227
• 发表日期: 2018
• 页码: 2243-2267
• 关键词: variable formula

摘要

The aim of this paper is to establish the weak convergence, in the topology of the Skorohod space, of the nu-symmetric Riemann sums for functionals of the fractional Brownian motion when the Hurst parameter takes the critical value H = (4l + 2)(-1), where l = l (.) = 1 is the largest natural number satisfying integral(1)(0) alpha(2j) nu(d alpha) = 1/2j+1 for all j = 0,..., l - 1. As a consequence, we derive a change-of-variable formula in distribution, where the correction term is a stochastic integral with respect to a Brownian motion that is independent of the fractional Brownian motion.