Pré-Publication, Document De Travail Année : 2025

Forward stochastic integration for adapted processes w.r.t. Riemann-Liouville fractional Brownian motion (Full version)

Résumé

This paper provides the time-dependent $L^2$-martingale representation of the forward stochastic integral where the driving noise is the Riemann-Liouville fractional Brownian motion with parameter $\frac{1}{2} < H < 1$ and the integrand is a square-integrable adapted process. As a by-product, we obtain the exact $L^2$-isometry of the forward stochastic integrals based on suitable conditions on time-dependent martingale representations of adapted integrands combined with the Nelson's stochastic derivative of the underlying Gaussian driving noise.

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Dates et versions

hal-05428334 , version 1 (22-12-2025)

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Paulo Henrique da Costa, Alberto Ohashi, Francesco Russo. Forward stochastic integration for adapted processes w.r.t. Riemann-Liouville fractional Brownian motion (Full version). 2025. ⟨hal-05428334⟩
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