Forward stochastic integration for adapted processes w.r.t. Riemann-Liouville fractional Brownian motion (Full version)
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866909962602545152 |
|---|---|
| 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 |