The L 2 -norm of the forward stochastic integral w.r.t. fractional Brownian motion H > 1 2

soumis
Type de publication :
Article (revues avec comité de lecture)
HAL :
hal-04264824
arXiv :
assets/images/icons/icon_arxiv.png 2310.16232
Mots clés :
Gaussian processes; Fractional Brownian motion; Forward and Young integrals; Stochastic calculus.
Résumé :
In this article, we present the exact expression of the $L^2$-norm of the forward stochastic integral driven by the multi-dimensional fractional Brownian motion with parameter $\frac{1}{2} < H < 1$. The class of integrands only requires rather weak integrability conditions compatible w.r.t. a random finite measure whose density is expressed as a second-order polynomial of the underlying driving Gaussian noise. A simple consequence of our results is the exact expression of the $L^2$-norm for the pathwise Young integral.
BibTeX :
@article{Oha-Rus-2200,
    author={Alberto Ohashi and Francesco Russo },
    title={The L 2 -norm of the forward stochastic integral w.r.t. 
           fractional Brownian motion H > 1 2 },
    year={soumis },
    month={11},
}