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July 2018 Weak symmetric integrals with respect to the fractional Brownian motion
Giulia Binotto, Ivan Nourdin, David Nualart
Ann. Probab. 46(4): 2243-2267 (July 2018). DOI: 10.1214/17-AOP1227

Abstract

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 $H=(4\ell+2)^{-1}$, where $\ell=\ell(\nu)\geq1$ is the largest natural number satisfying $\int_{0}^{1}\alpha^{2j}\nu(d\alpha)=\frac{1}{2j+1}$ for all $j=0,\ldots,\ell-1$. 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.

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Giulia Binotto. Ivan Nourdin. David Nualart. "Weak symmetric integrals with respect to the fractional Brownian motion." Ann. Probab. 46 (4) 2243 - 2267, July 2018. https://doi.org/10.1214/17-AOP1227

Information

Received: 1 June 2016; Revised: 1 July 2017; Published: July 2018
First available in Project Euclid: 13 June 2018

zbMATH: 06919024
MathSciNet: MR3813991
Digital Object Identifier: 10.1214/17-AOP1227

Subjects:
Primary: 60F17 , 60G05 , 60G15 , 60H07

Keywords: fractional Brownian motion , Itô formula in law , Malliavin calculus , Stratonovich integrals

Rights: Copyright © 2018 Institute of Mathematical Statistics

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Vol.46 • No. 4 • July 2018
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