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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2605.12269 |
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| _version_ | 1866917486676410368 |
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| author | Balan, Raluca M. Garza, Jaime |
| author_facet | Balan, Raluca M. Garza, Jaime |
| contents | In this article, we construct an Itô integral with respect to a two-sided finite-variance Lévy process $\{L(x)\}_{x\in \mathbb{R}}$, without a Gaussian component. Using Rosenthal inequality for discrete-time martingales, we give an estimate for the $p$-th moment of this integral, for any even integer $p\geq 2$. Then, using Poisson-Malliavin calculus, we show that the Itô integral is an extension of the Hitsuda-Skorohod integral with respect to the compensated Poisson random measure associated to the Lévy process. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_12269 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Itô integral for a two-sided Lévy process Balan, Raluca M. Garza, Jaime Probability In this article, we construct an Itô integral with respect to a two-sided finite-variance Lévy process $\{L(x)\}_{x\in \mathbb{R}}$, without a Gaussian component. Using Rosenthal inequality for discrete-time martingales, we give an estimate for the $p$-th moment of this integral, for any even integer $p\geq 2$. Then, using Poisson-Malliavin calculus, we show that the Itô integral is an extension of the Hitsuda-Skorohod integral with respect to the compensated Poisson random measure associated to the Lévy process. |
| title | Itô integral for a two-sided Lévy process |
| topic | Probability |
| url | https://arxiv.org/abs/2605.12269 |