The L²-norm of the forward stochastic integral w.r.t. Fractional Brownian motion H > (1)/(2)

2023/10/24 by Alberto Ohashi, Ohashi, Alberto, Francesco Russo +1 · 1 citation
Decision Sciences · Economics, Econometrics and Finance · #FOS: Mathematics #Probability (math.PR) #Probability and Risk Models #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2310.16232

openalex publication_date 2023/10/24 · openalex created_date 2023/10/27 · openalex updated_date 2026/07/28

Abstract

In this article, we present the exact expression of the L²-norm of the forward stochastic integral driven by the multi-dimensional fractional Brownian motion with parameter (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 L²-norm for the pathwise Young integral.

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