The $L^2$-norm of the forward stochastic integral w.r.t. Fractional Brownian motion $H > \frac{1}{2}$

Alberto Ohashi; Francesco Russo

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arXiv · 2310.16232

The $L^2$-norm of the forward stochastic integral w.r.t. Fractional Brownian motion $H > \frac{1}{2}$

Alberto Ohashi·Francesco Russo

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Abstract

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.

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Alberto Ohashi, Francesco Russo. 2023-10-24. The $L^2$-norm of the forward stochastic integral w.r.t. Fractional Brownian motion $H > \frac{1}{2}$. https://arxiv.org/abs/2310.16232

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