THE L 2 -NORM OF THE FORWARD STOCHASTIC INTEGRAL W.R.T. FRACTIONAL BROWNIAN MOTION H > 1 2 - Archive ouverte HAL Access content directly
Preprints, Working Papers, ... Year : 2023

THE L 2 -NORM OF THE FORWARD STOCHASTIC INTEGRAL W.R.T. FRACTIONAL BROWNIAN MOTION H > 1 2

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 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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Dates and versions

hal-04264824 , version 1 (30-10-2023)

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Alberto Ohashi, Francesco Russo. THE L 2 -NORM OF THE FORWARD STOCHASTIC INTEGRAL W.R.T. FRACTIONAL BROWNIAN MOTION H > 1 2. 2023. ⟨hal-04264824⟩
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