m-order integrals and generalized Ito's formula; the case of a fractional Brownian motion with any Hurst index
type: Dataset
description: Given an integer m, a probability measure ν on [0,1], a process X and a real function g, we define the m-order ν-integral having as integrator X and as integrand g(X). In the case of the fractional Brownian motion B, for any locally bounded function g, the corresponding integral vanishes for all odd indices m>1/2H and any symmetric ν. One consequence is an Itô–Stratonovich type expansion for the fractional Brownian motion with arbitrary Hurst index 01/6.
landing page: 0020-2347
keyword: 60h05-60g15-60g18
keyword: fractional-brownian-motion
keyword: infoeu-reposemanticsarticle
keyword: itos-formula
keyword: journal-articles
keyword: m-order-integral
keyword: mathmath-prmathematics-mathprobability-mathpr
issued: 2026-05-07T23:50:13.205788
modified: 2026-05-07T23:50:13.205792
language: en
contact point: Organization
  fn: CCSD

test_moissonnage_selune
type: Agent

m-order integrals and generalized Ito's formula; the case of a fractional Brownian motion with any Hurst index
type: Distribution
format: HTML
access URL: https://hal.science/hal-00091310
issued: 2026-05-07T23:50:13.207559
modified: 2026-05-07T23:50:13.197248