2009/06/08 by Jérémie Unterberger, Unterberger, Jeremie · 1 citation
Economics, Econometrics and Finance · Mathematics · #05C05 #16W30 #60F05 #60G15 #60G18 #60H05 #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.0906.1416
openalex publication_date 2009/06/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
The main tool for stochastic calculus with respect to a multidimensional process B with small Hölder regularity index is rough path theory. Once B has been lifted to a rough path, a stochastic calculus -- as well as solutions to stochastic differential equations driven by B -- follow by standard arguments. Although such a lift has been proved to exist by abstract arguments \citeLyoVic07, a first general, explicit construction has been proposed in \citeUnt09,Unt09bis under the name of Fourier normal ordering. The purpose of this short note is to convey the main ideas of the Fourier normal ordering method in the particular case of the iterated integrals of lowest order of fractional Brownian motion with arbitrary Hurst index.