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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.12864 |
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| _version_ | 1866909962602545152 |
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| author | da Costa, Paulo Henrique Ohashi, Alberto Russo, Francesco |
| author_facet | da Costa, Paulo Henrique Ohashi, Alberto Russo, Francesco |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_12864 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Forward stochastic integration for adapted processes w.r.t. Riemann-Liouville fractional Brownian motion (Full version) da Costa, Paulo Henrique Ohashi, Alberto Russo, Francesco Probability 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. |
| title | Forward stochastic integration for adapted processes w.r.t. Riemann-Liouville fractional Brownian motion (Full version) |
| topic | Probability |
| url | https://arxiv.org/abs/2512.12864 |